Question

Use the method of separation of variables to find a general solution to the differential equation

y′=2xy+3y−4x−6.

Answer 1

y' = y(2x+3) - 2(2x+3)
y' = (y-2)(2x+3)
dy/(y-2) = (2x+3) dx
ln(y-2) = x^2+3x+C
y-2 = c e^(x^2+3x)
y = c e^(x^2+3x) + 2