Answer:
The solution of the differential equation is
Step-by-step explanation:
The differential equation is a first order separable ordinary differential equation (ODE). We know this because a separable first-order ODE has the form:
where <em>g(t)</em> and <em>h(y) </em>are given functions<em>. </em>
We can rewrite our differential equation in the form of a first-order separable ODE in this way:
Integrating both sides
The integral of left-side is:
The integral of right-side is:
We can join the constants, and this is the implicit general solution
If we want to find the explicit general solution of the differential equation
We isolate B
Recall the definition of |x|
So
where
Now B(1) =30 implies
And the solution is