Find a power series solution of the differential equation y" + 4xy = 0 about the ordinary point x = 0.

Step-by-step explanation:

Given differential equation is

We have to find the power series solution of given differential equation about the ordinary point x = 0.

Power series solution of any given differential equation can be given by

Now, by putting these values in equation (1), we have

for n = 0

for n = 1

for n = 2

for n = 3

for n=4

As we can see for

for even value of n i.e n = 2m where m is any integer.

for odd value of n i.e n =2m+1 , where m is any integer.

So, the power series solution about the ordinary point x=0, can be given by

its kinda hard to answer this when we dont have all the information that we need.