Recent questions tagged ch9

Eliminate arbitrary constant and obtain differential equation $x^2-y^2= a(x^2+y^2)^2$

asked Feb 7, 2014 by meena.p

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Solve: $(3xy+y^2)dx+(x^2+xy)dy=0 \qquad y(1)=1$

asked Feb 7, 2014 by meena.p

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Solve: $\large\frac{dy}{dx}=\frac{-\sqrt {1-y^2}}{x-e^{\Large\sin ^{-1}y}}$

asked Feb 7, 2014 by meena.p

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Solve : $y''+e^{2y}(y')^3=0$

asked Feb 7, 2014 by meena.p

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Find general solution of equation $y'-2y+a=0$ a=fixed

asked Feb 7, 2014 by meena.p

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Find all values of m for which $y-e^{mx}$ is solution of equation $y'''-2y''-y'+2y=0$

asked Feb 7, 2014 by meena.p

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Which of following satisfy the differential equation $y'+2xy=0?$

asked Feb 7, 2014 by meena.p

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Which of the following satisfy differential equation $(1- \sin x) ^2 y''=\cos x$

asked Feb 7, 2014 by meena.p

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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.

asked Feb 7, 2014 by meena.p

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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

asked Feb 7, 2014 by meena.p

1 answer

Solve : $\log \bigg(\large\frac{1}{x}.\frac{dy}{dx}\bigg)$$=2x+5y$

asked Feb 7, 2014 by meena.p

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Form a differential equation represent family of curve given by $y= (c_1+c_2) -\sin (x+c_3)-c_4 e^{x+c_5}$

asked Feb 7, 2014 by meena.p

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Solve : $ \bigg(4 \sin ^{-1} \log \bigg(\large\frac{d^4y}{dx^4}\bigg)\bigg)^3=x+y^2$

asked 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$

asked Feb 7, 2014 by meena.p

1 answer

Solve : $ x \large\frac{dy}{dx}- \frac{y}{2}$$=x(\sin ^{-1}x) y^5$

asked Feb 6, 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$

asked 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$

asked Feb 6, 2014 by meena.p

1 answer

Solve : $y' +\tan x.y =\tan x \quad y(\large\frac{\pi}{4})$$=1$

asked 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$

asked Feb 6, 2014 by meena.p

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Solve : $\large\frac{dy}{dx}$$=\sqrt {16 x^2 y -4x^2 y^2}\qquad y(2)=1$

asked Feb 6, 2014 by meena.p

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Solve : $(x^2+1) dy =(4x+xy^2)dx$

asked Feb 6, 2014 by meena.p

1 answer

Solve : $e^x y dx=(e^{2x}+1) dy \quad y \cos =1$

asked Feb 6, 2014 by meena.p

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$y=e^{(t+2)x}$ is a solution of equation $\large\frac{d^2y}{dx^2}-\frac{4dy}{dx}$$+4y=0$ then t equals

asked Feb 6, 2014 by meena.p

1 answer

Find solution : $\large\frac{dy}{dx} $$= 1+ \sqrt {y-x+3}$

asked Feb 6, 2014 by meena.p

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Find solution : $\large\frac{dy}{dx}$$=y (x^2y^2-1)$

asked Feb 6, 2014 by meena.p

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Find the solution : $ x^2y'=1-xy$

asked Feb 6, 2014 by meena.p

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Find the solution : $-x dy +(y+\sqrt {xy})dx=0$

asked Feb 6, 2014 by meena.p

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Determine functions $y= 2e^{-x}+ 3e^{2x}$ is solution to which of following differential equation

asked 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$

asked 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 $xy''+2y''=0$

asked Feb 6, 2014 by meena.p

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Find the curve $y= f(x) $ through the origin for which $y''=y'$ and tangent at origin is $y=x$

asked Feb 6, 2014 by meena.p

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Find all curves in x-y plane such that tangent at each point (x,y) of curves intersects the x-axis at $(x-1,0)$

asked Feb 6, 2014 by meena.p

1 answer

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

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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

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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

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