What is the solution for (d^2+4)*y=x^2 ?

The solution for (d^2+4)*y=x^2 is y=c_{1}cos(2x)+c_{2}sin(2x)+(x^2)/4-1/8

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(d^2+4)*y=x^2

(d^{2} + 4) \cdot y = x^{2}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{x ^{2}}{4} - \frac{1}{8}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{x ^{2}}{4} - \frac{1}{8}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{x ^{2}}{4} - \frac{1}{8}

(d^{2} - d - 2) y = 2 lo g_{10} (x) + \frac{1}{x} + \frac{1}{x ^{2}}

y^{^{''}} - y = x^{2} \cdot e^{x} + 5

y^{^{''}} + 5 y^{^{'}} + 6 y = 5 sin (x)

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3} x

(d^{4} - 1) y = e^{x} cos (x)

What is the solution for (d^2+4)*y=x^2 ?
The solution for (d^2+4)*y=x^2 is y=c_{1}cos(2x)+c_{2}sin(2x)+(x^2)/4-1/8