00:01
Hello, the question is taken from a differential equation and in this question we have to solve this differential equation using the power series method.
00:11
So given the equation is d2y over dx square plus y is equal to 0 in order to solve it, let y is equal to, let its solution is of type y is equal to summation of n, cn, x to the power n.
00:28
Okay.
00:28
Where n belongs to 0 to infinity okay so if y is this then d y over d x will be equal to summation n c n into n x to the power n minus 1 okay this is a second term when and okay and in the similar way d2 y over d x square is n into n minus 1 summation over n cn x to the power and minus 2.
01:08
Substituting this value in the equation, we get n into n minus 1, summation over n, cn, x to the power n minus 2 plus submission over n, n into, sorry, submission over n, cn, x to the power n, that is equal to 0.
01:31
So in order to solve it, we need to equate the equal coefficient of a basically the equal coefficient of this x to the power n so let for this term n is equal to n plus 2 so we get n plus 2 n plus 1 c and plus 2 and this become n and this is also n plus cn so so if there is a minus there must be a minus here...