- #1
KevinD6
- 10
- 0
Homework Statement
If y = y(t) is the solution of the initial value problem
y' + (2 t + 1) y = 2 cos(t)
y(0) = 2
What is y''(0)?
Homework Equations
The Attempt at a Solution
Since this is a first order linear, I started out by finding the integrating factor so I can find what y is, and then just take the second derivative of it, and then put it to 0.
[itex] IF = e^{ \int {2t + 1} } => IF = e^{t^2 + t} [/itex]
Then, I end up with this equation, if we set IF = k.
[itex] (ky)' = k (2 cos(t)) [/itex]
From here, I don't think I can integrate that equation, so now I'm pretty much stuck. Is there a method I'm missing? Or could I find the value of the second derivative using the value of y at 0?
Any help is appreciated, thank you.