In differential equation show that it is homogeneous and solve it. x^2dy/dx + y^2 = xy ​

Question

In differential equation show that it is homogeneous and solve it.

x²\(\frac{dy}{dx}\) + y² = xy

Answer 1

⇒ \(\frac{dy}{dx}\) = \(\frac{xy-y^2}{x^2}\)

= \(\frac{y}{x}\) - \((\frac{y}{x})^2\)

⇒ \(\frac{dy}{dx}\) = \(f\frac{y}{x}\)

⇒ 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

e^x/y = xc