Solve the given differential equation. (The form of yp is given.)D2y - 2Dy + y = 2x + x2 + sin 5x(Let yp = A + Bx + Cx2 + E sin 5x + F cos 5x.)

A. y = c₁e^x + c₂xe^x + 10 + 6x + x² +  sin 5x +  cos 5x
B. y = c₁e^x + 10 + 6x + x² -  sin 5x +  cos 5x
C. y = c₁e^x + c₂xe^x + 10 + 6x + x² -  sin 5x +  cos 5x
D. y = c₁e^x + c₂xe^x + 10 + 6x + x² -  cos 5x +  sin 5x

Answer: C

Mathematics

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