In each of the following differential equation show that it is homogeneous and solve it.
(x³ + 3xy²)dx + (y³ + 3x²y)dy = 0

Question

In each of the following differential equation show that it is homogeneous and solve it. (x 3 + 3xy 2 )dx + (y 3 + 3x 2 y)dy = 0

Philoid · Accepted Answer

⇒ the given differential equation is a homogenous equation.

The solution of the given differential equation is :

Put y = vx

Integrating both the sides we get:

Resubstituting the value of y = vx we get

⇒ y⁴ + 6x²y² + x⁴ = C

Ans: y⁴ + 6x²y² + x⁴ = C

In each of the following differential equation show that it is homogeneous and solve it.(x3 + 3xy2)dx + (y3 + 3x2y)dy = 0