- #1
VeganGirl
- 10
- 0
Homework Statement
Solve the IVP, [tex]\frac{1}{4}[/tex]y'' + 16y = 0
y(0)=[tex]\frac{1}{4}[/tex]
y'(0)=0
Answer is given... y(t) = [tex]\frac{1}{4}[/tex]cos 8t
Homework Equations
The Attempt at a Solution
This has the characteristic equation [tex]\frac{1}{4}[/tex] [tex]\lambda[/tex]^2 +16[tex]\lambda[/tex]=0
Solving for lambda, I got [tex]\lambda[/tex]= 0 or -64
Therefore y(t) = A*e^(0t) + B*e^(-64t) for some constants A and B
[tex]\Rightarrow[/tex] y(t) = A + B*e^(-64t)
I know that I'll have to impose the initial conditions to get the specific solution, but my general solution is very different from the answer given. What am I doing wrong?