Recent questions tagged differential-equations

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 $t \to \infty$

asked 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 ?

asked 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 ?

asked Feb 6, 2014 by meena.p

1 answer

Observation show that rate of change of atmosphere pressure P with attitude h is proportional to pressure. Assume that pressure at 6000 meter is half of its value $P_0$ at sea level, find formula for pressure at any height.

asked Feb 6, 2014 by meena.p

1 answer

The growth rates of a bacteria population is proportional to its size. Initially the population is $10,000$ while after 10 days its size is $25,000$ . What will be population after 20 days?

asked Feb 6, 2014 by meena.p

1 answer

find value of $K_1$ and $K_2$ for which $y= \large\frac{x}{K_1} $$+K_2$ is a solution of differential equation $y''-2y' -3y=x$

asked Feb 6, 2014 by meena.p

1 answer

The degree and order of differential equation of family of parabolas whose length of latus rectum is fixed and axis is x-axis ,are respectively

asked Feb 5, 2014 by meena.p

1 answer

Find the solution : $y (\log x-1) y dx=x dy $

asked Feb 5, 2014 by meena.p

1 answer

Solve and get solutions : $ \bigg( x +y \large\frac{dy}{dx}\bigg)=\bigg( y -x \large\frac{dy}{dx}\bigg) \bigg(x^4+\large\frac{y^6}{x^2}$$+3 (x^2y^2+y^4)\bigg)$

asked Feb 5, 2014 by meena.p

1 answer

Solution of differential equation $\large\frac{dy}{dx} +\frac{y}{x}$$=x^3 y^5$ is which of the following?

asked Feb 5, 2014 by meena.p

1 answer

The solution of differential equation $(x^2-1) \large\frac{dy}{dx}$$+2xy =\large\frac{1}{x^2-1}$

asked Feb 5, 2014 by meena.p

1 answer

Which of the following equation is linear ?

asked Feb 5, 2014 by meena.p

1 answer

The graph of the function $y=f(x)$ passing through the point $(0,1)$ and satisfy the differential equation $\large\frac{dy}{dx}$$+y \cos x =\cos x $ is such that

asked Feb 5, 2014 by meena.p

1 answer

Which one of the following curves represents the solution of the initial value problem $y= D(e^x-1)$ where $D= \large\frac{dy}{dx}$ and $y(0)=50$

asked Feb 5, 2014 by meena.p

1 answer

The general solution of the differential equation $\large\frac{dy}{dx}=\frac{-y}{x}$ is a family of curves which looks most like which of the following

asked Feb 5, 2014 by meena.p

1 answer

The general solution of the differential equation $\large\frac{dy}{dx}=\frac{1-x}{y}$ is a family of curves which looks most like which of the following?

asked Feb 5, 2014 by meena.p

1 answer

General solution of differential equation $\large\frac{dy}{dx}=\frac{x}{2a}$

asked Feb 5, 2014 by meena.p

1 answer

The general solution of the given below differential equation is a family of curve where $4a$ is length of the latus rectum which looks $y \large\frac{dy}{dx}$$=2a$

asked Feb 5, 2014 by meena.p

1 answer

The differential equation for the family of curves $x^2+y^2-2ay=0$ where a is an arbitary constant is given $y'= \large\frac{dy}{dx}$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $r \sin \theta\; d\theta +(r^3 -2 r^2 \cos \theta +\cos \theta)dr=0$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{dy}{dx}$$=xe^{y-x^2}$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $(x+1) \large\frac{dy}{dx}$$-y = (x+1)^2$

asked Feb 4, 2014 by meena.p

1 answer

General solution of equations : $\large\frac{dy}{dx}$$+py=0$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{dy}{dx}=\frac{y+x-2}{y-x-4}$

asked Feb 4, 2014 by meena.p

1 answer

Solution of differential equation : $y(2xy+e^x)dx=e^xdy$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{dy}{dx} =\frac{2x+3y+6}{4x+6y+7}$

asked Feb 4, 2014 by meena.p

1 answer

Solution of differential equation : $\large\frac{dx}{dy}=\frac{y+x-2}{y+x+4}$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{dy}{dx}$$+x \sin 2y=x^3 \cos ^2 y$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $x \large\frac{dy}{dx}$$+y=x^3 y^6$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation : $(1+y^2)dx =(\tan^{-1}y -x)dy$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation ; $\large\frac{ydy}{xdx}+\frac{2(x^2+y^2)-1}{(x^2+y^2+1)}=0$

asked Feb 4, 2014 by meena.p

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$\large\frac{dy}{dx}$$=(4x+y+1)^2$ if $dy(0)=1$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equations: $\large\frac{dy}{dx}$$=e^{3x-2y}+x^2e^{-2y}$

asked Feb 4, 2014 by meena.p

1 answer

Differential equation of all circles radius 5, with their centres on the y-axis.

asked Feb 4, 2014 by meena.p

1 answer

General solution of following differential $\in a ^n$ differential equations of a family of circles passing through the origin and having centre on the x axis

asked Feb 3, 2014 by meena.p

1 answer

Different equation of all parabola with x axis as the axis and $(a,0)$ as the focus

asked Feb 3, 2014 by meena.p

1 answer

Differential equation of all parabola with x axis as the axis and 4a as latus rectum .

asked Feb 3, 2014 by meena.p

1 answer

The differential equation of the following equation $y=ae^{2x} +be^{-3 x} +ce^{x}$

asked Feb 3, 2014 by meena.p

1 answer

Solution of the general equation : $\large\frac{dy}{dx}$$=\cos (x+y) - \sin (x+y) $

asked Feb 3, 2014 by meena.p

1 answer

Find the degree of the following differential equation $\bigg(\large\frac{d^2 y}{dx^2}\bigg)^{1/2} =\bigg( \large\frac{dy}{dx}+3\bigg)^{1/3}$

asked Feb 3, 2014 by meena.p

1 answer

$\large\frac{dy}{dx} =\large\frac{y+x+1}{y+x +5}$

asked Feb 3, 2014 by meena.p

1 answer

Find the solution of differential equation : $\large\frac{dy}{dx}=\frac{x^2+y^2}{xy}$

asked Feb 3, 2014 by meena.p

1 answer

Let $g(n) $ is a continuous differential function which takes positive value for $ x \leq 0$ and satisfy $\int \limits_0^2 g(t) dt = x \sqrt {g(x)} $ with $f(1) =V_2$. find the value of $f(\sqrt 2 +1)$

asked Feb 3, 2014 by meena.p

1 answer

Given $y(0) =2000$ and $\large\frac{dy}{dx} =3200-20y^2$ then find the value of $\displaystyle\lim _{x \to \infty} y(n)$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation : $ (1-x^2)(1-y)dx -xy (1+y) dy=0$

asked Feb 3, 2014 by meena.p

1 answer

Solve: $xe^y dy -e^y dx=0$

asked Feb 3, 2014 by meena.p

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General solution of differential equation : $x^2e^y dy - (x-1) e^x dx=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation $x dy -y dx=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation : $x dy +y dx=0$

asked Feb 3, 2014 by meena.p

1 answer

2 separate reservation of oil A and B (capacity of $A=2 \times $ capacity of B) are filled completely with oil and oil is released simultaneously from both the reservoirs. The rate of flow of oil out of each reservoir at an instant of time is proportional to the quantity of oil in the reservoir at that time one hour after the oil is released the quantity of oil in reservoir A is 1.5 times the quantity of oil in reservoir B. If the reservoirs have same quantity of oil after $t= \large\frac{\log a}{\log b -\log c}$ then $a+b-c$

asked Feb 3, 2014 by meena.p

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