An extended form of Clairaut's equation expressed by

y = xF(p) + f(p)

may be similarly solved by first differentiating in regard to p, when

it reduces to a linear equation of which x is the dependent and p the

independent variable; from the integral of this linear equation, and

the original differential equation, the quantity p is then to be

eliminated.

Other types of solvable differential equations of the first order are

(1)

Encyclopaedia Britannica, 11th Edition, "Diameter" to "Dinarchus" Volume 8, Slice 4 · 第 37 / 86 题