Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions with the solutions of the differential equation obtained using the method of section 4.3. try to explain any differences between the two forms of the solution. y'' − y' = 0

We can reduce the order of the ODE to make solving a bit less taxing. Let so that .

Then assume a solution of the form

Substituting into the ODE gives

The coefficients in the series are given according to

We can solve the recurrence exactly:

Then

and integrating both sides to solve for gives

(I don't know what method is apparently being used in Section 4.3...)

$15 each

step-by-step explanation:

$45/3 children= $15 each

no solution

step-by-step explanation:

there is not enough information in the problem to solve.