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