Solve the following differential equation:

[CBSE 2011]

Given,

⇒

⇒ …(1)

We can observe that the above differential equation is a homogeneous equation.

We can verify this by putting y = λx.

To solve a homogeneous differential equation, we put y = vx

∴

So equation 1 can be rewritten as -

⇒

⇒

⇒

Integrating both sides we get –

Use the formula:

⇒

⇒

⇒

∵ v = y/x

∴

⇒ Cx² = y + √(y²+x²) is the required solution for given differential equation.