Question

Solve: xdy – ydx = √(x² + y²)dx.

Answer 1

The given differential equation is 

xdy/dx = – y = √(x² + y²) 

log |v + √(1 + v²)| = log c + log |x| 

 v + √(1 + v²) = cx

 y + √(y² + x²) = cx² 

which is the required solution