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Isn't the general solution yh + yp? What am I doing wrong? Got everything else correct, but stuck on question d.

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  • $\begingroup$ Did you forgot $e^t$ (it should be $t^2 e^t$) $\endgroup$ – Arctic Char Oct 30 '19 at 2:35
  • $\begingroup$ I entered $$ c1e^t + c2te^t -2t + c1 -t^2e^t + c2$$ and it's still wrong $\endgroup$ – jimmy kudo Oct 30 '19 at 2:38
  • $\begingroup$ What about that $2t$? where does it come from? $\endgroup$ – Arctic Char Oct 30 '19 at 2:39
  • $\begingroup$ $$c1e^t + c2te^t -2te^t + c1 -t^2e^t + c2$$ is incorrect $\endgroup$ – jimmy kudo Oct 30 '19 at 2:40
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    $\begingroup$ Ok its y1u1 + u2y2 $\endgroup$ – jimmy kudo Oct 30 '19 at 3:05
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HINT

To start with, rearrange the given ODE in the following manner

\begin{align*} y^{\prime\prime} - 2y^{\prime} + y = (y^{\prime} - y)^{\prime} - (y^{\prime} - y) \end{align*}

Then make the substitution $u = y^{\prime} - y$, which reduces the problem to solving a first order ODE twice.

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  • $\begingroup$ I think I did all that in part a,b,c. $\endgroup$ – jimmy kudo Oct 30 '19 at 2:46
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The given answer is not correct.

Your $$y_h = c_1e^t+c_2te^t$$ is correct but the $y_p$ is not . To find $y_p$ they used the method of variation of parameters as explained in the solution but they have their $y_p$ incorrect. The correct $y_p=-t^2e^t$ does not need the $c_1$ and $c_2$ but it uses $u_1e^t+u_2te^t$ where $u_1$ and $u_2$ are found by the integrals.

The correct answer is $$y= c_1e^t+c_2te^t -t^2e^t $$

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