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Questions asked by sreemathi.v
Questions
9373
questions
1
answer selected
Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y'=e^x\;\sin x.$
cbse
class12
bookproblem
ch9
sec4
q15
p396
medium
sec-b
math
asked
Nov 30, 2012
1
answer
For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.
cbse
class12
bookproblem
ch9
sec4
q16
p396
medium
sec-b
math
asked
Nov 30, 2012
1
answer
Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve,the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
cbse
class12
bookproblem
ch9
sec4
q17
p396
easy
sec-a
math
asked
Nov 30, 2012
1
answer
At any point (x,y) of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3).Find the equation of the curve given that it passes through (-2,1).
cbse
class12
bookproblem
ch9
sec4
q18
p396
sec-b
math
asked
Nov 30, 2012
1
answer
In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$
cbse
class12
bookproblem
ch9
sec4
q20
p397
sec-c
math
asked
Nov 30, 2012
1
answer
The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3units and after 3seconds it is 6units.Find the radius of balloon after t seconds.
cbse
class12
bookproblem
ch9
sec4
q19
p396
sec-c
math
asked
Nov 30, 2012
1
answer
In a bank, principal increases continuously at the rate of $5\%$ per year. An amount of $Rs.1000$ is deposited with this bank, how much will it work after $10$ years $(e^{0.5}=1.648)$.
cbse
class12
bookproblem
ch9
sec4
q21
p397
sec-c
math
asked
Nov 30, 2012
1
answer
In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?
cbse
class12
bookproblem
ch9
sec4
q22
p397
sec-c
math
asked
Nov 30, 2012
1
answer
The general solution of the differential equation\(\frac{\large dy}{\large dx}=e^{x+y}\)is
cbse
class12
bookproblem
ch9
sec4
q23
p397
sec-b
math
asked
Nov 30, 2012
1
answer
Show that the differential equation is homogeneous and solve $(x^2+xy)\;dy=(x^2+y^2)\;dx$
cbse
class12
bookproblem
ch9
sec5
q1
p406
medium
sec-b
math
asked
Nov 30, 2012
1
answer
Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]
cbse
class12
bookproblem
ch9
sec5
q2
p406
easy
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]
cbse
class12
bookproblem
ch9
sec5
q3
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q4
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$
cbse
class12
bookproblem
ch9
sec5
q5
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $x\;dy-y\;dx=\sqrt{x^2+y^2}dx$
cbse
class12
bookproblem
ch9
sec5
q6
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$
cbse
class12
bookproblem
ch9
sec5
q7
p406
difficult
sec-b
math
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$
cbse
class12
bookproblem
ch9
sec5
q8
p406
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q9
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q11
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q12
p406
difficult
sec-b
math
asked
Nov 29, 2012
1
answer
Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q14
p406
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q15
p406
medium
modelpaper
2012
q19
sec-b
math
asked
Nov 29, 2012
1
answer
A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution
cbse
class12
bookproblem
ch9
sec5
q16
p406
easy
sec-a
math
asked
Nov 29, 2012
1
answer
Which of the following is a homogeneous differential equation?
cbse
class12
bookproblem
ch9
sec5
q17
p407
sec-a
easy
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $\large\frac{dy}{dx}$$+2y=\sin x$
cbse
class12
bookproblem
ch9
sec6
q1
p413
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$
cbse
class12
bookproblem
ch9
sec6
q2
p413
easy
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2$
cbse
class12
bookproblem
ch9
sec6
q3
p413
easy
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$
cbse
class12
bookproblem
ch9
sec6
q4
p413
easy
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$
cbse
class12
bookproblem
ch9
sec6
q5
p413
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$
cbse
class12
bookproblem
ch9
sec6
q6
p413
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$
cbse
class12
bookproblem
ch9
sec6
q7
p413
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$
cbse
class12
bookproblem
ch9
sec6
q8
p413
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$
cbse
class12
bookproblem
ch9
sec6
q9
p414
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$
cbse
class12
bookproblem
ch9
sec6
q10
p414
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$
cbse
class12
bookproblem
ch9
sec6
q11
p414
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation $(x+3y^2)\large\frac{dy}{dx}=y$$\;(y>0)$
cbse
class12
bookproblem
ch9
sec6
q12
p414
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$
cbse
class12
bookproblem
ch9
sec6
q13
p414
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find a particular solution satisfying the given condition $(1+x^2)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{1+x^2}$$;y=0\;when\;x=1$
cbse
class12
bookproblem
ch9
sec6
q14
p414
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$
cbse
class12
bookproblem
ch9
sec6
q15
p414
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Find the equation of curve passing through the origin given that the slope of the tangent to the curve at any point \((x,y)\) is equal to the sum of the coordinates of the point .
cbse
class12
bookproblem
ch9
sec6
q16
p414
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Find the equation of curve passing through the point(0,2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5
cbse
class12
bookproblem
ch9
sec6
q17
p414
math
sec-a
asked
Nov 29, 2012
1
answer
The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 $ is
cbse
class12
bookproblem
ch9
sec6
q18
p414
easy
math
sec-a
asked
Nov 29, 2012
1
answer
The integrating factor of the differential equation $(1-y^2)\large\frac{dx}{dy}$$+yx=ay\: \;is$
cbse
class12
bookproblem
ch9
sec6
q19
p414
easy
math
sec-a
asked
Nov 29, 2012
1
answer
verify that the given function (implicit or explicit) is a solution of the corresponding differential equation
cbse
class12
bookproblem
ch9
misc
q2
q2-1
p420
medium
math
sec-a
asked
Nov 29, 2012
1
answer
Form the differential equation representing the family of curves given by $(x-a)^2+2y^2\;=\;a^2$, where $a$ is an arbitrary constant
cbse
class12
bookproblem
ch9
misc
q3
p420
medium
sec-b
math
asked
Nov 29, 2012
1
answer
Prove that \(x^2-y^2\;=\;c(x^2+y^2)^2\)is the general solution of differential equation \((x^3-3x\;y^2)dx\;=\;(y^3-3x^2y)dy\) where \(c\) is a parameter.
cbse
class12
bookproblem
ch9
misc
q4
p420
difficult
math
sec-b
asked
Nov 29, 2012
1
answer
Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
cbse
class12
bookproblem
ch9
misc
q5
p420
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$
cbse
class12
bookproblem
ch9
misc
q6
p420
easy
math
sec-b
asked
Nov 29, 2012
1
answer
Show that the general solution of the differential equation\(\large\frac{dy}{dx}+\large\frac{y^2+y+1}{x^2+x+1}=0\) is given by \((x+y+1)\;=\;A(1-x-y-2xy)\), where A is parameter
cbse
class12
bookproblem
ch9
misc
q7
p420
medium
math
sec-b
asked
Nov 29, 2012
1
answer
Find the equation of the curve passing through the point\(\bigg(0,\large\frac{\pi}{4}\bigg)\) whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$
cbse
class12
bookproblem
ch9
misc
q8
p420
easy
math
sec-b
asked
Nov 29, 2012
1
answer
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