SCALC8 9.5.024. My Notes A Bernoulli differential equation (named after James Bernoulli) is of the form dy dx + P(x)y = Q(x)yn. Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = y1 − n transforms the Bernoulli equation into the linear equation du dx + (1 − n)P(x)u = (1 − n)Q(x). Use the substitution u = y1 − n to solve the differential equation. xy' + y = −5xy2