What is the solution for (d^2+1)*y=x*cos(x) ?

The solution for (d^2+1)*y=x*cos(x) is y=c_{1}cos(x)+c_{2}sin(x)+(x^2sin(x))/4+(xcos(x))/4

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(d^2+1)y=xcos(x)

(d^{2} + 1) \cdot y = x \cdot cos (x)

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x ^{2} sin ( x )}{4} + \frac{x cos ( x )}{4}

Solution steps

(d^{2} + 1) y = x cos (x)

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x ^{2} sin ( x )}{4} + \frac{x cos ( x )}{4}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{x ^{2} sin ( x )}{4} + \frac{x cos ( x )}{4}

(d^{2} - 4 d + 4) y = e^{2} x + sin^{2} (x)

(d^{2} - 1) \cdot y = x \cdot sinh (x)

y^{^{''}} + y = 12 x

y^{^{''}} + 4 y = 2, e^{x} y (0) = 2, y^{^{'}} (0) = 1

(d^{2} - d - 2) y = 10 cos (x)

What is the solution for (d^2+1)*y=x*cos(x) ?
The solution for (d^2+1)*y=x*cos(x) is y=c_{1}cos(x)+c_{2}sin(x)+(x^2sin(x))/4+(xcos(x))/4