Estimation would give you an answer close to the actual answer so you can see if your answer is reasonable depending on how close the estimate is
Squaring both sides of the given equation: w^2=7w, or w^2-7w=0.
w^2-7w=0 can be factored: w(w-7)=0. Then, w=7 or w=0. Both 0 and 7 are solutions of this equation.
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:
