Differential Eq...

Solution of the differential equation: $$\left( 2xcosy+{ y }^{ 2 }cosx \right) dx+\left( 2ysinx-{ x }^{ 2 }siny \right) dy=0$$ is :

Solution of the equation $$\dfrac{{dy}}{{dx}} = 1 + xy + x + y$$ is

The general solution of the differential equation $$\dfrac { dy }{ dx } +y={ x }^{ 3 }$$ is ______.

Solution of differential equation $$ \cfrac {dy} {dx} + x{sin}^{2} y $$= $$sin y  \quad cos y  \quad $$is

If $$\dfrac{dy}{dx}=y+3>0$$ and $$y(0)=2$$ then $$y(\ln{2})$$ is equal to :

The general solution of the differential equation $$e^xdy+(ye^x+2x)dx=0$$ is

The solution of differential equation $$\cos x.\sin y dx+\sin x. \cos ydy=0$$ is 

For the given differential equation find the general solution:

The differential equation of the system of circles touching the $$x$$-axis at origin is  

Let y=y(x) be the solution of the differential equation $$sinx\dfrac { dy }{ dx } +ycosx=4x,x\in (0,\pi )$$. If $$y=\left( \dfrac { \pi  }{ 2 }  \right) =0,then\quad y\left( \dfrac { \pi  }{ 6 }  \right) $$ is equal to :