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Recent questions and answers in Differential Equations
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JEEMAIN and NEET
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Mathematics
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Class12
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Differential Equations
If the marginal cost of manufacturing a product is $C' = 3 + 0.25x$, find the total cost of function $C$ given that $C(0) = 60$.
jeemain
math
class12
ch9
differential-equations
apllication-of-diffrential-equation
difficult
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
The rate at which the population of a bacteria culture grows is proportional to the number of bacteria present. If the number of bacteria grew from $1000$ to $5000$ in $10$ hours find the number of bacteria after $15$ hours
jeemain
math
class12
ch9
differential-equations
application-of-differential-equation
difficult
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to number of inhabitants, find the number of years in which the population would treble itself?
jeemain
math
class12
ch9
differential-equations
difficult
applications-of-differential-equations
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
Find the general solution of $xy' - 2y = x^2$
jeemain
math
class12
ch9
differential-equations
solving-using-separation-of-variables
easy
answered
Mar 20, 2014
by
balaji.thirumalai
1
answer
The tangent to a curve intersects x axis at $B$ and $y$ at $A$. The normal to same curve intersects $x$ axis at $C$ and $Y$ axis at $D$. Given $\large\frac{AO}{OB}= \frac{OC}{CD}$ curve passes through $(2,3)$. Find the curve
jeemain
math
class12
ch8
application-of-integrals
area-between-two-curves
q100
difficult
answered
Feb 10, 2014
by
meena.p
1
answer
Equation of conic defined by : $9yy'+4x=0 $ and given $y(0)=2$, find length of latus rectum
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q99
medium
answered
Feb 10, 2014
by
meena.p
1
answer
Equation of conic defined by : $9yy'+4x=0 \qquad y(0)=2$ find length of latus rectum
jeemain
math
class12
unit10
differential-equations
q99
medium
asked
Feb 10, 2014
by
meena.p
0
answers
$\large\frac{dy}{dx}$$=1$ passes through $\large[$$0,\large\frac{3}{2}]$ and $ \large\frac{dy}{dx}$$=2$ passes through $[0,1]$ represents two curve which passes through a point whose coordinates are zeroes of a quadratic polynomial . The quadratic equation is gradient polynomial. Find sum of coefficients of $x^3,x^2,x$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q98
difficult
answered
Feb 7, 2014
by
meena.p
1
answer
A tank contains $200\; gal$ of water of $40\; lb$ salt dissolves. $5\; gal$ of brine , each containing $2\; lb$ of dissolved salt, run into tank per minute and mixture kept uniform by stirring runs out at same rate. Find amount of salt $y(t)$ in tank at any time $(t)$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q97
difficult
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $2e^{\Large\frac{x}{y}}(dx-dy)+dx-2e^{\Large\frac{x}{y}} \large\frac{x}{y}$$dy=0$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q96
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $y'= 1+y^2$
jeemain
math
class12
ch9
differential-equations
linear-differential-equations
q95
easy
answered
Feb 7, 2014
by
meena.p
1
answer
The two curves represents by $9yy'+4x=0,\; y(0)=2,\; yy'+x=0,\; y(0)=3$ then number of common normals for two curves will be
jeemain
math
class12
ch9differential-equations
linear-differential-equations
q94
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find solution of differential equation $(y-x+1) dy -(y+x+2)dx=0$
jeemain
math
class12
ch9
differential-equations
linear-differential-equations
q93
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find solution : $(x-2y+1) dy -(3x-6y+2)dx=0$
jeemain
math
class12
ch9
differential-equations
linear-differential-equations
q92
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Eliminate arbitrary constant and obtain differential equation $x^2-y^2= a(x^2+y^2)^2$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q91
medium
mock
answered
Feb 7, 2014
by
meena.p
1
answer
Solve: $(3xy+y^2)dx+(x^2+xy)dy=0 \qquad y(1)=1$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q90
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Solve: $\large\frac{dy}{dx}=\frac{-\sqrt {1-y^2}}{x-e^{\Large\sin ^{-1}y}}$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q89
difficult
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $y''+e^{2y}(y')^3=0$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q88
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find general solution of equation $y'-2y+a=0$ a=fixed
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q87
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find all values of m for which $y-e^{mx}$ is solution of equation $y'''-2y''-y'+2y=0$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q86
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Which of following satisfy the differential equation $y'+2xy=0?$
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q85
easy
answered
Feb 7, 2014
by
meena.p
1
answer
Which of the following satisfy differential equation $(1- \sin x) ^2 y''=\cos x$
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q84
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find nature of curve not passing through origin for which tangent at any point P. on curve is equal to radius vector of point P.
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q83
difficult
answered
Feb 7, 2014
by
meena.p
1
answer
The largest internal for which solution of differential equation $\large\frac{dy}{dx}=\sqrt {\large\frac{1-y^2}{(1+x^2)^2}}$ where $y(0)= \large\frac{1}{\sqrt 2}$ holds good is
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q82
difficult
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $\log \bigg(\large\frac{1}{x}.\frac{dy}{dx}\bigg)$$=2x+5y$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q81
easy
answered
Feb 7, 2014
by
meena.p
1
answer
Form a differential equation represent family of curve given by $y= (c_1+c_2) -\sin (x+c_3)-c_4 e^{x+c_5}$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q80
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $ \bigg(4 \sin ^{-1} \log \bigg(\large\frac{d^4y}{dx^4}\bigg)\bigg)^3=x+y^2$
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q79
easy
answered
Feb 7, 2014
by
meena.p
1
answer
Find the order and degree of differential equation : $e^{\Large\frac{d^6y}{dx^6}}-x^2 \large\frac{d^4y}{dx^4}$$+y=0$
jeemain
math
class12
ch9
differential-equations
order-and-degree-of-a-differential-equation
q78
easy
answered
Feb 7, 2014
by
meena.p
1
answer
Solve : $ x \large\frac{dy}{dx}- \frac{y}{2}$$=x(\sin ^{-1}x) y^5$
jeemain
math
class12
ch9
differential-equations
solving-using-separation-of-variables
q77
medium
answered
Feb 7, 2014
by
meena.p
1
answer
Find the solution : $ (1+x^4) \large\frac{dy}{dx}$$-4x^3y =(x^5+x) \tan ^{-1} (x^2) \qquad y(1)=\pi$
jeemain
math
class12
ch9
differential-equations
solving-using-separation-of-variables
q76
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Solve: $ (e^x+e^{-x} )\large\frac{dy}{dx}$$=1- \large\frac{(e^x+e^{-x})^2}{(e^x-e^{-x})}$$y$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q75
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Solve : $y' +\tan x.y =\tan x \quad y(\large\frac{\pi}{4})$$=1$
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q74
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Find the solution : $\large\frac{\sqrt x -2}{\sqrt y -1}$$dy =\large\frac{\sqrt y+1}{\sqrt x +2}$$dx$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q73
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Solve : $\large\frac{dy}{dx}$$=\sqrt {16 x^2 y -4x^2 y^2}\qquad y(2)=1$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q72
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Solve : $(x^2+1) dy =(4x+xy^2)dx$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q71
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Solve : $e^x y dx=(e^{2x}+1) dy \quad y \cos =1$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q70
medium
answered
Feb 6, 2014
by
meena.p
1
answer
$y=e^{(t+2)x}$ is a solution of equation $\large\frac{d^2y}{dx^2}-\frac{4dy}{dx}$$+4y=0$ then t equals
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q69
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Find solution : $\large\frac{dy}{dx} $$= 1+ \sqrt {y-x+3}$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q68
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Find solution : $\large\frac{dy}{dx}$$=y (x^2y^2-1)$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q67
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Find the solution : $ x^2y'=1-xy$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q66
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Find the solution : $-x dy +(y+\sqrt {xy})dx=0$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q65
difficult
answered
Feb 6, 2014
by
meena.p
1
answer
Determine functions $y= 2e^{-x}+ 3e^{2x}$ is solution to which of following differential equation
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q64
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Solve : $ y dx +x dy +\sin y \cos ^2 (xy) dy+e^x \cos^2 (xy) dx=0$
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q63
difficult
answered
Feb 6, 2014
by
meena.p
1
answer
Find curve in $x-y$ plane which passes through$(1,1)$ . Intersects line $y=x$ at right angle at that point and satisfies $xy''+2y''=0$
jeemain
math
class12
ch9
differential-equations
linear-differential-equations
q62
medium
answered
Feb 6, 2014
by
meena.p
1
answer
Find the curve $y= f(x) $ through the origin for which $y''=y'$ and tangent at origin is $y=x$
jeemain
math
class12
ch9
differential-equations
linear-differential-equations
q61
difficult
answered
Feb 6, 2014
by
meena.p
1
answer
Find all curves in x-y plane such that tangent at each point (x,y) of curves intersects the x-axis at $(x-1,0)$
jeemain
math
class12
ch9
differential-equations
ordinary-differential-equations
q60
easy
answered
Feb 6, 2014
by
meena.p
1
answer
Find all curves in x-y plane such that tangent at each point (x,y) of curves intersects the x-axis at $(x-1,0)$
jeemain
math
class12
unit10
differential-equations
q60
easy
asked
Feb 6, 2014
by
meena.p
0
answers
The initial value problem governing the current i following in an RL circuit when a step voltage of magnitude $\in$ is applied to circuit at $t=0$ is given by (R, L, t are constants ) $iR= \large\frac{Ldi}{dt} $$=\in, t > 0, i(0)=0$ Determine limiting value of i as $t \to \infty$
jeemain
math
class12
ch9
differential-equations
solving-using-separation-of-variables
q59
medium
answered
Feb 6, 2014
by
meena.p
1
answer
A ratio active substance dis integrals at a rate proportional to amount of substance present. $50 \%$ of amount disintegrates in $1000$ years. Approximately what $\%$ of substance will disintegrate in $50$ years ?
jeemain
math
class12
ch9
differential-equations
homogeneous-differential-equations
q58
medium
answered
Feb 6, 2014
by
meena.p
1
answer
A drop of liquid evaporates at a rate proportional to its area of surface. If the radius initially is $4\;mm$ and $5$ minutes later, the radius is reduced to $2\; mm$, find radius of drop as a function of time ?
jeemain
math
class12
ch9
differential-equations
formation-of-differential-equations
q57
medium
answered
Feb 6, 2014
by
meena.p
1
answer
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