Differential Eq...

Solution of differential equation $$\sin y.\dfrac {dy}{dx}+\dfrac {1}{x}\cos y=x^{4}\cos^{2}y$$ is

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

The value of the constant $$'m'$$ and $$'c'$$ for which $$y=mx+c$$ is a solution of the differential equation $$D^2y-3Dy-4y=-4x$$.

The solution of the differential equation $${ 2x }^{ 2 }y\dfrac { dy }{ dx } =tan\left( { x }^{ 2 }{ y }^{ 2 } \right) -{ 2xy }^{ 2 }$$ given $$y(1)=\sqrt { \dfrac { \pi  }{ 2 }  } $$ is

The solution of the equation $$(x^2 +xy)dy=(x^2+y^2)dx $$is 

Solve the given differential equation $$\dfrac{dy}{dx}=(cosx-sinx),$$

Which of the following functions is differentiable at x=0?

The solution of the differential equation $$x\dfrac{dy}{dx}=y(log y-log x+1)$$ is

If $$\cos { x } \cfrac { dy }{ dx } -y\sin { x } =6x,(0<x<\cfrac { \pi  }{ 2 } )$$ and $$\quad y\left( \cfrac { \pi  }{ 3 }  \right) =0\quad $$ then $$y\left( \cfrac { \pi  }{ 6 }  \right) $$ is equal to:

Solution of the differential equation of $${ (y }^{ 2 }-{ x }^{ 3 })dx-xydy=0\quad $$ is