Question

Solve : \( p^{2} y+2 p x=y \)

Answer 1

The given differential equation is 

p²y + 2px = y ...(i)

2px = y – p²y

x = (y – p²y)/2p

Differentiating, w.r.t. y, we get

py = c ...(ii)

Eliminating p between Eqs (i) and (ii), we get 

y² + 2cx = c²

which is the required solution.