Agohofidov6

Answered

2022-01-21

Particular solution to $y{}^{\u2033}-3{y}^{\prime}+2y=2{e}^{x}$

Answer & Explanation

limacarp4

Expert

2022-01-21Added 39 answers

Use operator D:

Let

So,

ambarakaq8

Expert

2022-01-22Added 31 answers

This is too long for a comment, so I posted it as an answer. First solve for the homogeneous equation

Let me do another example: to solve

First solve the homogenous equation

RizerMix

Expert

2022-01-27Added 437 answers

The simplest thing in your case is probably to use this (easily justified) trick: If p(x) is a one variable polynomial with complex coefficients and c a complex number, then the ODE
$p(\frac{d}{dx})y={e}^{cx}$
has a solution of the form ${e}^{cx}q(x)$ where q(x) is a polynomial whose degree is the number of roots of p(x) equal to c.
In you case, $p(x)=(x-1)(x-2),c=1$ , so the trick tells you to look for a solution of the form
$(ax+b){e}^{x}$ ,
and you can clearly assume $b=0$ .

Most Popular Questions