Differential Eq...

If $$y=y\left( x \right) $$ and $$\displaystyle \frac { 2+\sin { x }  }{ y+1 } \left( \frac { dy }{ dx }  \right) =-\cos { x } ,y\left( 0 \right) =1$$, then find the value of $$\displaystyle y\left( \frac { \pi  }{ 2 }  \right) $$.

Solution of differential equation $$sec\, x\, dy - cosec\, y \,dx = 0$$ is

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

General solution of $$y\dfrac{dy}{dx}+by^2 = a \cos x, 0 < x < 1$$ is:

The solution of the differential equation $$\displaystyle\frac{d^{2}y}{dx^2}+3y=-2x$$ is.

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

The differential equation $$y\dfrac{dy}{dx}=a-x$$ represents

 A particle, initially at origin moves along $$x$$ axis according to the rule $$\dfrac{dx}{dt}=x+4$$. The time taken by the particle to traverse a distance of $$96$$ units is

Consider the differential equation $${ y }^{ 2 }dx+\left( x-\cfrac { 1 }{ y }  \right) dy=0$$. If $$y(A)=1$$, then $$x$$ is given by

The solution of $$e^{2x-3y}dx+e^{2y-3x}dy=0$$ is