Equations Solvable for x:

Consider the given differential equation on solving for x is expressible as

x = ƒ(y, p).                               (i)

differentiating (i) w.r.t. y, we get an equation of the form

Suppose the solution of (ii) is ψ (x, p, c) = 0                  (iii)

The needed solution is calculated by wither removing p between (i) and (iii) or expressing (i) and (iii) as

x = g₁ (p, c), y = g₂ (p, c); p being a parameter.