- Let be a function such that
Let and show that satisfies

for constants . Determine the values of the constants.

- Find a solution .

**Incomplete.**

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#
Stumbling Robot

A Fraction of a Dot
#
Find solutions of a differential equation of a given form

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

- Let be a function such that
Let and show that satisfies

for constants . Determine the values of the constants.

- Find a solution .

**Incomplete.**

a.) From our givens, we have

We are to find constants a and b such that

Written another way, simplifying terms:

We can satisfy this equation with the following constants

b.) Now, to find a solution to the above second order equation of the form Cx^n

From part (a.) we found the values of constants a and b. We can plug in these values to give our second-order equation, and since the solution y is of the form Cx^n, we have

And, the equation

Becomes

Assuming a nontrivial solution, we can divide both sides by Cx^n

This quadratic equation is satisfied by

Giving us

And from our givens, we know that

Thus,