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...)

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.