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

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.