Question

find solution of given D.E. dy/dx = -(x²+3y²)/(3x²+y²)

Answer 1

We have

dy/dx = -(x² + 3y²)/3x² + y²

Put y = vx

By multiplying with (v + 1)³ 

3 + v² = A(v + 1)² + B(v + 1) + C 

v = –1 ⇒ 3 + 1 = C ⇒ C = 4 

Equating the co-efficients of v² 

A = 1 

Equating the co-efficients of v 

0 = 2A + B 

B = –2A = –2