Frobenius method problems with trigonometric coefficients and indicial equation

[edgar]

i need your help...i had to solve some ode using the frobenius method but half-way through i stuck...
for the first ode
i didn't know what to do when i had to multiply the sinx and cosx with y,y',y"
ii)i had a problem because of the cosx and i couldn't equate the series...--->second ode
iii)a) the third is to be solved using frobenius, but a1 has a problem...,
b) by using y(x)=w(x)/x, i had to find the new solution
oh and x0=0
the ode formulas are attached...forgive me i am not a native english speaker and it is the first time i write in this kind of forum...also please help me as much as you can...i have a deadline until tommorow...thanks again...

 

[HallsofIvy]

Since you are writing y as a Taylor's series, do the same with sine and cosine.