What is the solution for (d^2-2d+3)y=x^2 ?

The solution for (d^2-2d+3)y=x^2 is y=e^x(c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x))+(x^2)/3+(4x)/9+2/27

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(d^2-2d+3)y=x^2

(d^{2} - 2 d + 3) y = x^{2}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{3} + \frac{4 x}{9} + \frac{2}{27}

Solution steps

(d^{2} - 2 d + 3) y = x^{2}

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{3} + \frac{4 x}{9} + \frac{2}{27}

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{2}}{3} + \frac{4 x}{9} + \frac{2}{27}

What is the solution for (d^2-2d+3)y=x^2 ?
The solution for (d^2-2d+3)y=x^2 is y=e^x(c_{1}cos(sqrt(2)x)+c_{2}sin(sqrt(2)x))+(x^2)/3+(4x)/9+2/27