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## Homework Statement

Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

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- Thread starter peace-Econ
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Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

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Can you solve this de:

y'' - 4y' + 4y = e

and if so, what method would you use?

Hint: This isn't an idle question.

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HallsofIvy

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## Homework Statement

Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

## Homework Equations

## The Attempt at a Solution

Do you know what the "characteristic equation" of a linear differential with constant coefficients is? Such an equation will have [itex]e^{ax}[/itex] and [itex]e^{bx}[/itex] as independent solutions if and only if its characteristic equation is [itex](r- a)(r- b)= 0[/itex].

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