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find the differential solution to the equation to which the given function is the general solution y=(A+Bx+Cx^2)e^(2x)

Differential Equations
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I don't understand the question. What are we supposed to do?
I guess, you want to find out the function? if so, from your general solution, I expand it to \(y= Ae^{2x}+ Bxe^{2x}+Cx^2e^{2x}\) that shows you have \(\lambda =2\) triple roots so, the characteristic equation is \((\lambda -2)^3 =0\) and then \(= \lambda^3 -6\lambda^2+12\lambda -8 =0\) that gives us the original function is y''' -6y''+12y' -8y =0 that's all I know. Hope this help
i figure it out thank you i was suppose to find the equation it was y'''-6y''+8y'-8y=0

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12y' , not 8y'
I just seen that thank you
ok
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