Differential Eq...

The solution of the differential equation $$x \, dx + y\, dy = x^2y\, dy - y^2\, x\, dx$$ is

Solve differential equation $$dx=\dfrac{xdv}{v^2-a^2}$$.

Solution for $$\dfrac{x + y \dfrac{dy}{dx}}{y - x \dfrac{dy}{dx}} = x^2 + 2y^2 + \dfrac{y^4}{x^2}$$ is 

The particular solution of the differential equation $$y(1+\log x)\dfrac{dx}{dy} -x =0$$ when $$x=e, y=e^2$$ is

Solution of differential equation $$xdy-yx=0$$ represents:

The solution of $$\dfrac{{dy}}{{dx}} = \dfrac{{x{{{\mathop{\rm log x}\nolimits} }^2} + x}}{{\sin y + y\cos y}}$$

The solution of $$\cos \, y \, \log (\sec \, x + \tan \, x) dx = \cos \, x \, \log (\sec \, y + \tan \, y) dy$$ is 

The equation of the curve through $$\left(0, \dfrac{\pi}{4} \right)$$ satisfying the differential equation. $$e^x \, \tan \, y \, dx + (1 + e^x) \sec^2 \, ydy = 0$$ is given by 

The solution to the differential equation $$\cos\ xdy=y(\sin x-y)dx$$, $$0<x<\dfrac{\pi}{2}$$, is

If $$\phi \left( x \right) =\phi \prime \left( x \right) $$ and $$\phi \left( 1 \right) =2$$, then $$\phi \left( 3 \right) $$ equals