WW3 - Problem 4

[Diane Sicsic]

Hey guys! I'm working on WW3 Problem 4 (it's a second order with constant coefficient homogeneous differential equation, its solution, y(t)'s value at 0 and its limit, and we're supposed to find c1 and c2). The only equation I find involving c1 and c2 is c1+c2=4, but when I try to imput y(t) with the values c1=2 and c2=2, it says my answer is wrong.
Does anyone know how to get the answer?

[Adam Gregg]

The general solution is $y(t)=c_1e^{3t}+c_2e^{-3t}$. When solving for $c_1$ and $c_2$ you should get $c_1=0$ since the problem states that $y(t) \to 0$ as $t\to  +\infty$
Sufficient would be to spume only that $y(t)$ is bounded as $t\to +\infty$. So condition at $+\infty$ replaces one condition at $0$.--V.I.
Also $c_1+c_2=8$ for the given condition of $y(0)=8$.

Therefore $c_2=8$ and $y(t)=8e^{-3t}$.

Actually similar problem from the TextBook already was discussed.