Find the solution to the differential equation
db/dt+4b=20
with b(1)=30

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 g(t) and h(y) are given functions.

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