Answer:
Step-by-step explanation:
This is <em>a separable differential equation</em>. Rearranging terms in the equation gives
Integration on both sides gives
where is a constant of integration.
The steps for solving the integral on the right hand side are presented below.
Therefore,
Multiply both sides by
By taking exponents, we obtain
Isolate .
Since when
, we obtain an initial condition
.
We can use it to find the numeric value of the constant .
Substituting for
and
in the equation gives
Therefore, the solution of the given differential equation is