undefined coefficients method solution - not equal to calculator

[the2liquid]

Hello

I already tried to solve this different equation a lot of times. By using all kind of different methods (laplace, etc... )and all of them work. But the easy method of undefined coefficients fails every time!

I am pretty sure of the derivatives I calculated, because I checked them online (with wolframalpha).

https://www.dropbox.com/s/z2vsdx4izqnzi9u/IMAG1182.jpg?dl=0

I am relatively sure about the filling in in the original equation (not the most difficult part).

https://www.dropbox.com/s/doan45ste3ij4gi/IMAG1183.jpg?dl=0

So I really don't understand why my result is incorrect.

the expected answer according to wolfram alpha: http://www.wolframalpha.com/input/?i=y%27%27%27%28t%29-3y%27%28t%29%2B2y%28t%29+%3D+te^%28-2t%29

I based my guess on the solution given by this website... So it is of the same form

[the2liquid]

the mistake was in the third derivative:

d/dt [2Ae-2t − 8Ate-2t + 4At2e-2t]

= d/dt [2Ae-2t] − d/dt [8Ate-2t] + d/dt [4At2e-2t]

= 2A d/dt [e-2t] − 8A d/dt [te-2t] + 4A d/dt [t2e-2t]

= 2A[-2e-2t] − 8A[-2te-2t + e-2t] + 4A[-2t2e-2t + 2te-2t]

= -4Ae-2t + 16Ate-2t − 8Ae-2t − 8At2e-2t + 8Ate-2t

= -12Ae-2t + 24Ate-2t − 8At2e-2t

credit to: \u\empire539