y"'-3y"-3y'=x^2e^x where y(0)=1, y'(0)=2, y"(0)=0
show step
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arrggh, you will have to type them in as
d^3y/dt^3 -3 d^2y/dt^2-3dy/dt
and
t^2 e^t
In case you don't have an online calculator handy,
L{1} = 1/s
L{e^t} = 1/(s-1) = F(s)
L{t^2 e^t} = (-1)^2 F"(s) = 2/(s-1)^3
L{y} = f(s)
L{y'} = sf(s)-f(0) = sf(s)-1
L{y"} = s^2f(s)-sf(0)-f'(0) = s^2f(s)-s+2
L{y'"} = s^3f(s)-s^2f(0)-sf'(0)-f"(0) = s^3f(s)-s^2+2s
Put that all together and you get
(s^3f(s)-s^2+2s)-3(s^2f(s)-s+2)-3(sf(s)-1) = 2/(s-1)^3
f(s) =
s^5-8s^4+21s^3-25s^2+14s-1
------------------------------------
s(s-1)^3 (s^2-3s-3)
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