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General solution means, solving the homogenous differential equation, setting \(g(x)=0 \)

To find \(g(x)\) you can just take the inverse of the right hand side.

Can you check one answer?
\[\Large e^{-3t}+xe^{-3t}+e^{-t}-e^{-6t}+C \]
C not yet calculated.

my guess is that only the first two are right, given by the homogenous system.

whats C?

you cant get partial credit so I can only check it at the end

hehe I actually get C=0 for the one above, so something looks dodgy

no wait, C=1

ok let me check

since we have initial conditions.

it's wrong:(

did you correct the x? Of course it should be there (-:

the other solution I got was this one
\[\Large 16te^{-3t}+e^{-t}-e^{-6t} \]

ok let me check

it's wrong :(

yea but dont we stop there

\[\Large Y= \frac{e^{-s}}{(s+3)^2}- \frac{e^{-6s}}{(s+3)^2}+ \frac{16}{(s+3)^2} \]

yea thats what I got earlier and it was wrong

That's not the solution we've got to inverse it.

oh

So inverse that and you should get the solution

oh ok

try that and then please tell me if it's correct.

I did the step and it ended up being wrong

i ended up getting (e^(-3t))(-e^(18)(t-6)step(t-6)+e^(3)(t-1)step(t-1)+16t)

yea that doesnt work

I was checking on a similar problem and they attempt the problem the exact same way as we do.

i know thats what confused me! I did it twice and got the same asnwer

can your program read it? Or do you need to substitute something for the stepside function ??

i only have to substitute the theta to the wrod stepwhich i did and it was still wrong

somewhere in my notes I have an error.

yea

We are only two constants off but I can't see where I have made the algebraic error yet.

yeh I will.

thank you!

no problem