Question: I'm trying to solve for t given:
y''''(t)-10y'''(t)+35y''(t)-50y'(t)+24y(t) = e^(5t)
and that
y'''(0) = y''(0) = y'(0) = y(0) = 0
any hints??
Answer:
Thank you for your question. I don’t get a lot of cal. questions…so this will be fun!
In general, when we’re dealing with finding higher order derivatives, it is important to simplify the process in your mind by only thinking in terms of first order derivatives. In other words,
f'' (x) = f ' (f ' (x) )
Or in words, “the 2nd derivative of x is the derivative of the first derivative”
“the 3nd derivative of x is the derivative of the 2nd derivative”
Etc…
Also, look at the given information:
y'''(0) = y''(0) = y'(0) = y(0) = 0
Why was this given? What information does this give you that is necessary to solve for t?
Next, the exponential term is a real headache. How could you eliminate it?
I hope this helps. If you need further help, you can email me or leave a comment to this post. I can provide a sample problem.
Thanks.
Mrs. Young
