We\'re given a general solution to a differential equation y\'\' - 25y = 0 that

Question

We're given a general solution to a differential equation y'' - 25y = 0 that is y=A*e^(5x)+B*e^(-5x). It asks us to find a specific solution that

y'' - 25y = 0

y(0)=5

lim y(x) goes to inf = 0

What I have so far, may or may not be right:

From the second parameter I get that A + B = 5, correct? And taking the limits seperately we find the B side does head to zero but the equation attached to the A side heads to infinity. I'm not sure how to "kill" this term, or alter it. Where should I be looking and do I have the right ideas so far?

Explanation / Answer

you are on the right path.

the only way it could posisble have a limit as y tends to infinity is when A=0 ( i.e there is no e^x term )

=>

B = 5

A =0, B = 5

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