Differential Eq...

Find the solution of  $$\displaystyle \frac{dy}{dx}=\frac{xy+y}{xy+x}$$

$$\displaystyle x\cos ^{2}ydx=y\cos ^{2}x dy$$

Solve the diffrential equation:  $$\displaystyle \log \frac{dy}{dx}=ax+by$$

Find the solution of  $$\displaystyle xy\frac{dy}{dx}=\frac{1+y^{2}}{1+x^{2}}\left ( 1+x+x^{2} \right )$$.

Find the solution of  $$\displaystyle a\left ( x\frac{dy}{dx}+2y \right )=xy\frac{dy}{dx}$$.

Find the solution of  $$\displaystyle \left ( x^{2}-yx^{2} \right )\frac{dy}{dx}+\left ( y^{2}+xy^{2} \right )=0$$

$$y=ae^{-1/x}+b$$ is a solution of $$\displaystyle\frac{dy}{dx}=\frac{y}{x^{2}}$$ when

Solution of the given differential equation $$\displaystyle \left ( 1-x^{2} \right )\frac{dy}{dx}+xy=xy^{2}$$ is

The order of the differential equation whose general solution is given by $$y =(C_1+ C_2 )\, cos\, (x+ C_3 )\, -\, C_4e^{x+c_5}$$ where $$C_1, C_2, C_3, C_4, C_5$$ are arbitrary constants, is:

Find the solution of  $$\displaystyle\frac{dy}{dx}+\sin\left ( \frac{x+y}{2} \right ) =\sin \left ( \frac{x-y}{2} \right )$$.