allerySolve dy/dx + y = sin x:
Ay = -x
By = sin x
Cy = cos x
Dy = (sin x - cos x)/2 + C e^(-x)
Answer & Solution
Correct answer: D. y = (sin x - cos x)/2 + C e^(-x)
Linear, P = 1, μ = e^x. (e^x y)' = e^x sin x.
∫e^x sin x dx = (e^x/2)(sin x - cos x).
So e^x y = (e^x/2)(sin x - cos x) + C
→ y = (sin x - cos x)/2 + C e^(-x).
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