Differential Equations - power series method

[IniquiTrance]

Homework Statement

Solve:

y'' + y' - 2y = 0

y(0) = 1
y'(0) = -2

Homework Equations

The Attempt at a Solution

I found:

http://image.cramster.com/answer-board/image/cramster-equation-200942414569633761817696516250247.gif

So the recurrence relation is:

http://image.cramster.com/answer-board/image/cramster-equation-20094241457286337618184812037502167.gif

for n = 0:

http://image.cramster.com/answer-board/image/cramster-equation-20094241458446337618192469850005024.gif

Now here's my question. Can I assume at this point that:

c₀ = y(0) = 1
and c₁ = y ' (0) = -2

?

This would allow me to have a numerical value for each c_n.

Thanks!

 

[Mark44]

Yes. Think about what your original power series for y(x) looked like. All the terms except the first had nonzero powers of x, so if x = 0, you have y(0) = c₀. Then, think about what y'(x) looks like. Same idea for c₁.

 

[IniquiTrance]

Thanks Mark. I was able to solve this by making the above assumption getting y(x) = e^-2x I just wasn't sure if I was permitted to make that assumption.