Tyra
2020-10-20
Answered

Find the general solution of $y{}^{\u2033}-2{y}^{\prime}+2y=x{e}^{x}\mathrm{cos}x$

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Aniqa O'Neill

Answered 2020-10-21
Author has **100** answers

Let

First solve the homogeneous equation:

The characteristic equation is

So

Use Euler’s expansion:

Let C=A+B and D=A-B, then:

Call this general solution

Now we have to deal with xeˣc, the particular solution, which will give us y₂, such that the entire solution is

We guess the solution, where P, Q, R and S are constants:

Let

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