Consider y &#x2033; </msup> + y = 2 x sin &#x2061;<!-- ⁡ -->

hornejada1c 2022-07-11 Answered
Consider
y + y = 2 x sin ( x )
I have the solution for the homogeneous equation. Now i am trying to guess a particular solution for: 2 x sin ( x )
My first guess was: ( A x + B ) cos x + ( C x + D ) sin x but i end up with the system:
{ 2 A + 2 B = 0 2 C = 0
Then my quess was: ( A x 2 + x B ) cos x + ( C x 2 + x D ) sin x but that leaves me with:
{ A x B + 4 C = 0 2 A 2 D = 0 4 A C x D = 0 2 B 2 C = 0
Is here something wrong?
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Answers (1)

Kroatujon3
Answered 2022-07-12 Author has 19 answers
The last guess is true but your calculations are incorrect.
The final equation should give.
2 A + 2 D = 0 2 B + 2 C = 0 4 A = 2 4 C = 0
Thus C = B = 0 , A = D = 1 2
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