In each of the question, show that the given differential equation is homogeneous and solve each of them.

Question

In each of the question, show that the given differential equation is homogeneous and solve each of them. (x 2 + xy)dy = (x 2 + y 2 )dx

Philoid · Accepted Answer

Here, putting x = kx and y = ky

= k⁰.f(x,y)

Therefore, the given differential equation is homogeneous.

(x² + xy)dy = (x² + y²)dx

To solve it we make the substitution.

y = vx

Differentiating eq. with respect to x, we get

Integrating on both side,

- v - 2log|1 - v| = log|x| + logc

The required solution of the differential equation.