Chapter 6.4, Problem 63E

To determine

To calculate: The general solution of the Bernoulli equation $y^{\prime }-y=e^x\sqrt[3]{y}$ granted that the general solution of the Bernoulli equation $y^{\prime }+P\left(x\right)y=Q\left(x\right)y^n$ is $y^{\left(1-n\right)}{e}^{{\displaystyle \int \left(1-n\right)P\left(x\right)dx}}={\displaystyle \int \left(1-n\right)Q\left(x\right)e^{{\displaystyle \int \left(1-n\right)P\left(x\right)dx}}}dx+C$