Differential Eq...

Let $$y=y(x)$$ be the solution of the differential equation $$\sin x\dfrac {dy}{dx}+y\cos x=4x,x\ \in\ (0,\pi)$$, if $$y\left(\dfrac {\pi}{2}\right)=0$$, then $$y\left(\dfrac {\pi}{6}\right)$$ is equal to

The solution of equation $$\dfrac { dy }{ dx } =\dfrac { 1 }{ x+y+1 } $$

The solutions of the differential equation  $$\frac{dy}{dx}= \frac{siny+x}{sin2y-x cos y }$$ is 

Solution of differential equation $$xdy=(y-{x}^{2}-{y}^{2})dx$$ is (where $$c$$ is arbitrary constant)

The general solution of the differential equation $$\dfrac{dy}{dx} + \sin \dfrac{x+y}{2} = \sin \dfrac{x-y}{2}$$ is

The solution of differential equation,$$\left(x+\tan y\right)dy=\sin 2y\,dx$$ is

If the general solution of the differential equation if $$y'=\frac { y }{ x } +\Phi \left( \frac { x }{ y }  \right) $$, for some function $$\Phi $$, is given by $$yin|cx|=x$$, where c is an arbitrary constant, then $$\Phi $$ (2) is equal to :

If a curve $$y=f(x)$$ passes through the point $$(1,-1)$$ and satisfies the differential equation, $$y(1+xy)dx=xdy$$, then $$f\left(-\dfrac {1}{2}\right)$$ is equal to

General solution of differential equation $$x^{2}(x+y\frac{dy}{dx})+(x\frac{dy}{dx}-y)\sqrt{x^{2}+y^{2}}=0$$ is

Solution of differential equation $${ x }^{ 6 }dy+3{ x }^{ 5 }ydx=xdy-2y\ dx$$ is