Equations Solvable for p:

Let the equation F (x, y, p, ...., pn) = 0 on operating for p is expressible as

(p - ƒ₁) (p - ƒ₂) .... (p - ƒ_n) = 0,

Where ƒ_i's are functions of y and x. Then

P - ƒ_i = 0, I = 1, 2, ...., n

Or, dy/dx = ƒ_i(x, y), I = 1, 2, ....., n

which may be calculated by the methods defined earlier. If Ø_i (x, y, c_i) = 0 is the solution of p - ƒ_i = 0 for i = 1, 2, ...., n, the solution of the provided differential equation is of the form

Ø₁ (x, y, c₁) . Ø₂ (x, y, c₂) ..... Ø_n (x, y, c_n) = 0.

Since a differential equation of the first order has only one arbitrary constant, the basic solution of the provided equation will be of the form

Ø₁ (x, y, c) . Ø₂ (x, y, c) ..... Ø_n (x, y, c_n) = 0.