Answer:

Step-by-step explanation:

This is a homogeneous linear equation. So, assume a solution will be proportional to:

Now, substitute
into the differential equation:

Using the characteristic equation:

Factor out 

Where:

Therefore the zeros must come from the polynomial:

Solving for
:

These roots give the next solutions:

Where
and
are arbitrary constants. Now, the general solution is the sum of the previous solutions:

Using Euler's identity:


Redefine:

Since these are arbitrary constants

Now, let's find its derivative in order to find
and 

Evaluating
:

Evaluating
:

Finally, the solution is given by:

Answer:
y = 2x -8
Step-by-step explanation:
Answer:
Width = 4m
Length = 12 m.
Step-by-step explanation:
Let width = x, then length = 3x.
Perimeter
= 2(3x + x) = 32
2 * 4x = 32
x = 32 / 8 = 4 m.
The length = 3*4 = 12m and width = 4 m.