Differential Eq...

The solution of $$xdx+ydy=\frac { xdy-ydx }{ { x }^{ 2 }+{ y }^{ 2 } } $$ is ________________________.

The solution of the differential equation $$(x^2-yx^2)\dfrac{y^3}{x}=k+y^2+xy^2=0$$ is?

Let $$f\left( x \right) ={ cos }^{ -1 }\left( cosx \right)$$ then 

differential equation of all parabolas whose axis s y - axis.......

$$Let_y-y(x)$$ be the solution of the differential
equation $$sinx\dfrac{dy}{dx} -ycosx -4x,_x\epsilon (0,\pi ). if y\left(\frac{\pi}{2}\right)$$ = 0,
then y $$\left(\dfrac{\pi}{6}\right)$$ is equal to 

Integrating factors of the differential equation $$\frac{{dy}}{{dx}} + y = \frac{{1 + y}}{x}$$ is 

Solution of the differential equation $$\left( { x }^{ 2 }+1 \right) y'+2xy=4{ x }^{ 2 }$$ is 

Consider the differential equation, $$ydx-(x+y^{2})dy=0$$. If for $$y=1$$, x takes value $$1$$, then value of $$x$$ when $$y=4$$ is:

The differential equation found by the elimination of the arbitrary constant K from the equation $$y=(x+K)e^{-x}$$ is

The solution of the differentiable equation $$x^{2}\dfrac {dy}{dx}.\cos \dfrac {1}{x}-y\sin \dfrac {1}{x}=-1$$, where $$y\rightarrow -1$$ as $$x\rightarrow \infty$$ is