What is the solution for x^{''}-6x^'+13x=2197t^2 ?

The solution for x^{''}-6x^'+13x=2197t^2 is x=e^{3t}(c_{1}cos(2t)+c_{2}sin(2t))+169t^2+156t+46

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x^{''}-6x^'+13x=2197t^2

x^{^{''}} - 6 x^{^{'}} + 13 x = 2197 t^{2}

x = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 169 t^{2} + 156 t + 46

Solution steps

x^{''} (t) - 6 x^{'} (t) + 13 x = 2197 t^{2}

Solve linear ODE:

x = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 169 t^{2} + 156 t + 46

x = e^{3 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + 169 t^{2} + 156 t + 46

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

y^{^{''}} + 2 y^{^{'}} + 5 = e^{x}

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{3 x} cos (2 x)

y^{^{''}} = 2 y^{^{'}} + 15 y + sin (3 t)

y^{^{''}} - 6 y^{^{'}} + 8 y = - 2 e^{2 t}

What is the solution for x^{''}-6x^'+13x=2197t^2 ?
The solution for x^{''}-6x^'+13x=2197t^2 is x=e^{3t}(c_{1}cos(2t)+c_{2}sin(2t))+169t^2+156t+46