In differential equation show that it is homogeneous and solve it.xdy/dx - y = 2√ {y^2 - x^2}

Question

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

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

xdy/dx - y = 2√ {y² - x²}

Answer 1

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

⇒ 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

Ans: y + \(\sqrt{y^2-x^2}\) = c|x|³