Differential Eq...

The solution of the differential equation $$ \frac { d y } { d x } - k y = 0 , y ( 0 ) = 1 $$, approaches zero when $$ x \rightarrow \infty , $$ if

Solve the differential equation:
$$(e^ {y}+1)\cos x\ dx+e^ {y}\sin x\ dy=0$$

Solution of differential equation $$  \frac{d y}{d x}+x \sin ^{2} y=\sin y \cos y  $$ is-

The solution of $$y^5x+y-x\dfrac{dy}{dx}=0$$ is

Suppose y=y(x) satisfies the differential equation $$ydx+y^{2}dy=xdy.$$ If $$y(x) > 0 \forall x\epsilon R$$ and y(1)=1, then y(-3) equals

$$y = (c_{1} + c_{2}x + x^{2}) e^{x}$$ is a solution of

Solution of the differential equation
$$x=1+\left(xy\dfrac{dy}{dx}\right)+\dfrac{(x^2y^2)}{2!}\left(\dfrac{dy}{dx}\right)^3+.........$$ is

$$y=3\sqrt{2x}$$  Find  $$\frac{dy}{dx}$$

Solution of differential equation $$2xy \dfrac {dy}{dx} = x^{2} + 3y^{2}$$.

The solution of $$\dfrac{dy}{dx}+\dfrac{x}{1-x^{2}}y=x\sqrt{y}$$, is given by