Chapter 6.4, Problem 61E

Solving a Bernoulli Differential Equation In Exercises 57-64, solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form

$y^{\text{'}}+P(x)y=Q(x)y^n$

that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is

$y^{1-n}{e}^{f(1-n)P\left(x\right)dx=}{\displaystyle \int (1-n)Q(x)e^{f(1-n)P\left(x\right)dx}dx+C}.$

$x{y}^{\text{'}}+y=x{y}^3,x>0$