Chapter 6.5, Problem 63E

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

$y^{\prime }+P(x)y=Q(x)y^{″}$

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

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

$y^{\prime }-y=e^x\sqrt[3]{y}$