21. Solve be separable method
To solve the differential equation by separable method, we need to rearrange it so that all the terms are on one side and all the terms are on the other side. Then, we can integrate both sides to obtain the solution.
First, we can divide both sides by to get
Now, we can integrate both sides with respect to their respective variables:
To integrate the left-hand side, we can use the substitution , which gives us and . Substituting these expressions and using the identity , where is the constant of integration, we get:
To integrate the right-hand side, we can simply use the power rule:
Therefore, the general solution to the differential equation is:
where is an arbitrary constant of integration.