Question

In problems 13 to 15, find a solution (or solutions) of the differential equation not obtainable by specializing the constant in your solution of the original problem. Hint: See Example 3

Problem 11

Short answer

The solution is y=2.

Step-by-step solution

Given Information.

Differential Equation given is $2y\text{'}=3{\left(y-2\right)}^{\frac{1}{3}}$

Definition of Differential equation

A differential equation is an equation that contains at least onederivativeof an unknown function, either an ordinary derivative or a partial derivative.

Solve differential equation

Separate the variables in problem 11 to get

$\frac{dy}{{\left(y-2\right)}^{\frac{1}{3}}}=\frac{3}{2}dx$

The general solution of this differential equation is

$y={\left(x+C_1\right)}^{\frac{3}{2}}+2$

Now,$\frac{dy}{y^2}$is not valid for y=2

y=2 is a solution of this differential equation that cannot be obtained by any choice of $C_1$

Therefore, the solution is y=2 .