Question

Find the general solution to the differential equation:

yy’ – x2 = 3.

Answer 1

yy' - x^2 = 3

1/2 (2y y') = (x^2+3)
(y^2)' = 2 (x^2+3)
y^2 = 2/3 x^3 + 3x + C
= 2/3 (x(x^2+9)+C)
y = ±√(2/3) √(x(x^2+9)+C)