Question

In Problems, 31-34 verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a power

Short answer

Answer:

Therefore, differentiate the given power series and substitute it into the given equation.

Step-by-step solution

Given Information

The given differential equation is;

and

To differentiate the given power series.

Differentiating the given power series, we obtain

Use the Substitution method.

We substitute (1) and (2) into the given differential equation.

Find the series

For the first series, we letThe summation becomes

For the first series, we letThe summation becomes

For the first series, we letSo,

Hence, we get:

The given power series is the solution of the given equation.