Question

solve for the two power series solution of the given differential equation: y"+x^2y=0

Answer 1

do you have boundary (or initial) condition ?

Answer 2

\[y=c_0+c_1x+c_2x^2+c_3x^3+c_4x^4+c_5x^5+...\\y''=2c_2+3*2c_3x+4*3c_4x^2+5*4c_5x^3+...\\x^2y=c_0x^2+c_1x^3+c_2x^4+...\\ \rightarrow c_4=-\frac{c_0}{4*3}\\c_5=-\frac{c_1}{5*4}\\c_6=-\frac{c_2}{6*5}\\c_{n}=-\frac{c_{n-4}}{n(n+1)}\]

Answer 3

thanks! i got it :)