0

First of all, the image is my question page. enter image description here

Then, I have my answer for this question just don't know if it is right or not. If I am wrong, can you give me a suggestion? enter image description here

Irregular User
  • 3,862
Hao
  • 13
  • 2

1 Answers1

0

You reach this equation: $$ \sum_{n=0}^\infty(b-n)a_nx^n=0 $$ So $(b-n)a_n=0$ for every n. Hence, if b is not a natural number, then all $a_n$ are 0. And if $b$ is an integer then $a_b$ can be chosen arbitrarly so the solution would be: $$ y=\left\{\begin{array}{cc}a_bx^b & b\in\mathbb{N}\\0&\text{otherwise} \end{array}\right. $$

David Jaramillo
  • 1,117