Solve the following differential equations :

Here, 2xydx + ( x² + 2y² ) dy = 0

It is a homogeneous equation

Put y = vx

And

So,

Integrating Both Sides we get,

…… (1)

1 + 2v² = A – 2Av² + Bv² + cv

1 + 2v² = v²( – 2A + B) + cv + A

Comparing the coefficients of like power of v,

A = 1

C = 0

– 2A + B = 2

– 2 + B = 2

B = 4