The presence of nonlinear terms prevents us from using the technique of this section. In s...

The presence of nonlinear terms prevents us from using the technique of this section. In special cases, a change of variable will transform the nonlinear equation into one that is linear. The equation known as Bernoulli’s equation,

was proposed for solution by James Bernoulli in December 1695. In 1696, Leibniz pointed out that the equation can be reduced to a linear equation by taking x1–n as the dependent variable. Show that the change of variable, z = x1–n, will transform the nonlinear Bernoulli equation into the linear equation

Hint: If z = x1–n, then