How do you even do this?! i’m so confused
1 answer:
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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: