Recent content by teddy_boo

Oh, everything's okay now, I was able to get the answer. Haha, I'm an idiot. My problem's easily remedied by just expanding the series further. Thanks anyway :smile:

After expansion, I don't know how to factor x^3 and x^5 terms.

Here's another way to put it upon expansion: (2a_2+6a_3 x+12a_4 x^2+⋯)+(3a_1+6a_2 x+9a_3 x^2+⋯)+(2a_0+2a_1 x+2a_2 x^2+⋯)=x-x^3/3!+x^5/5!+⋯

Okay, so here's the equation: ∑_(i=2)^∞▒〖i(i-1) a_i x^(i-2)+3∑_(i=1)^∞▒〖ia_i x^(i-1)+2∑_(i=0)^∞▒〖a_i x^i=∑_(i=0)^∞▒(〖(-1)〗^i x^(2i+1))/(2i+1)!〗〗〗

Yes, I'm aware it could be solved analytically. My problem lies with the fact that after having changed the entire expression into power series, I'm totally blank on what to do next. The power series for the sine function is complicated relative to the one for y and its derivatives. I'm...

Oh, I'm so sorry, let me edit the post for a while

Homework Statement y"+3y'+2y= sin x y(0)=0 y'(0)=1 Evaluate y(0.1) Homework Equations Power Series Equation The Attempt at a Solution

Hey there! I'm new here and I just want to ask anyone willing how to solve this problem using power series: y"+3y'+2y= sin x y(0)=0 y'(0)=1 Evaluate y(0.1) Thanks! :smile: