Question

calc help

Answer 1

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Answer 2

i am only in 6th grade i can't help with this one lol srry

Answer 3

help?

Answer 4

what methods do you know? laplace transform maybe?

Answer 5

we can narrow some of it down logically if need be

Answer 6

too late

Answer 7

for instance e^-2t would have to derive down to 1/4 e^-2t, so to held constant at y'' it wold have to start as 4e^-2t

Answer 8

had a little minor logical flaw lol

e^-2t comes from 1/4 e^-2t by default

Answer 9

Would integrating both sides work? Sorry it's been a while since I've been in DE.

Answer 10

\[L(y'')=L(e^{-2t})+10L(e^{4t})\]
\[s^2L(y)-sy(0)-y'(0)=\frac{1}{s-2}+\frac{10}{s+4}\]
\[s^2L(y)-s(1)-0=\frac{1}{s-2}+\frac{10}{s+4}\]
\[L(y)=\frac{1}{s^2(s-2)}+\frac{10}{s^2(s+4)}+\frac{1}{s}\]
assuming i remember how to run a laplace on e^at

Answer 11

1/(s-a) sooo close :)

\[L(y)=\frac{1}{s^2(s+2)}+\frac{10}{s^2(s-4)}+\frac{1}{s}\]

but all thats just showing off :)