- #1
cragar
- 2,552
- 3
Homework Statement
Show that the imaginary part of the solution of
[itex] z''+z'+z=te^{it} [/itex] is a solution of [itex] y''+y'+y=tsin{t} [/itex]
The Attempt at a Solution
Ok so I first make the guess that [itex] z(t)=(at+b)e^{it} [/itex]
then I find z' and z'' and plug it back in and then equate the coefficients of t and then all the leftover constants.
I do this and I get a=-i and b=(2i+1)
so then I plug this in back to the original guess for z(t) and then multiply it by Eulers formula
and then take the imaginary part and see if it works for y(t). Is this the right approach.
I seem to be off by a cosine factor, I could post my work, but I just wanted to know if this is the right approach.