Question

Solve: (y + 1)P – xP² + 2 = 0. 

Answer 1

The given differential equation can be written as

y = Px – (2/P) – 1 ...(i)

Differentiating w.r.t. x, we get

dP/dx = P + x(dP/dx) + ((2/P²)(dP/dx))

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

y = cx – (2/c) – 1 

which is the general solution of Eq. (i). 

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

(y + 1)² + 8x = 0

which is the singular solution of Eq. (i).