In each of the question, show that the given differential equation is homogeneous and solve each of them.
(x² + xy)dy = (x² + y²)dx

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.

In each of the question, show that the given differential equation is homogeneous and solve each of them.(x2 + xy)dy = (x2 + y2)dx