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find yp (particular integral)
(D2 + 4D + 5) y = 2 e-2xcos(x)
((D+2)(D+2)+1) y = 2 e-2xcos(x)
yp = [1/((D+2)2 + 1)] ⋅ 2e-2xcos(x)
yp = e(-3)x ∫ ∫ e-(-3)x⋅2e-2xcos(x)dxdx
yp = e(-3)x ∫ ∫ e3x ⋅ 2e-2xcos(x)dxdx
yp = e(-3)x ∫ (exsin(x)+excos(x))dx
yp = e(-3)x[-½ excos(x) + ½exsin(x) + ½exsin(x) + ½excos(x)]
yp = e(-3)x ⋅ ex sin(x)
yp = e(-2)x sin(x) ; this is my answer
But correct answer is x e(-2)x sin(x)
Why are there variables x ?
find yp (particular integral)
(D2 + 4D + 5) y = 2 e-2xcos(x)
((D+2)(D+2)+1) y = 2 e-2xcos(x)
yp = [1/((D+2)2 + 1)] ⋅ 2e-2xcos(x)
yp = e(-3)x ∫ ∫ e-(-3)x⋅2e-2xcos(x)dxdx
yp = e(-3)x ∫ ∫ e3x ⋅ 2e-2xcos(x)dxdx
yp = e(-3)x ∫ (exsin(x)+excos(x))dx
yp = e(-3)x[-½ excos(x) + ½exsin(x) + ½exsin(x) + ½excos(x)]
yp = e(-3)x ⋅ ex sin(x)
yp = e(-2)x sin(x) ; this is my answer
But correct answer is x e(-2)x sin(x)
Why are there variables x ?
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