Find a second-order lincar equation for which

Reuben Brennan 2022-03-25 Answered
Find a second-order lincar equation for which
y(x)=c1e3x+c2e5x+sin(2x)
is the general solution
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Answers (2)

haiguetenteme7zyu
Answered 2022-03-26 Author has 13 answers
The homogenous part of the linear equation is, c1e3x+c2e5x
The particular part of the linear equation is sin(2x)
From the homogenous part, it can be concluded that the roots of the characteristic equation will be 3 and 5.
Find the characteristic equation.
(m3)(m5)=0
m28m+15=0
Assume f(x) to be the right-hand side of the differential equation. The differential equation will be, y8y+15y=f(x)
Substitute y=sin2x which is the particular solution into the differential equation obtained.
d2sin(2x)dx28dsin(2x)dx+15sin(2x)=f(x)
4sin(2x)16cos(2x)+15sin(2x)=f(x)
16cos(2x)+11sin(2x)=f(x)
Thus, the differential equation will be,
y8y+15y=11sin(2x)16cos(2x)
Answer: y8y+15y=11sin(2x)16cos(2x)
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Jeffrey Jordon
Answered 2022-03-31 Author has 2262 answers

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