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

The solution for (d^2-2d+1)y=x^2e^2x is y=c_{1}e^x+c_{2}xe^x+e^2x^3+6e^2x^2+18e^2x+24e^2

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(d^2-2d+1)y=x^2e^2x

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

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2} x^{3} + 6 e^{2} x^{2} + 18 e^{2} x + 24 e^{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2} x^{3} + 6 e^{2} x^{2} + 18 e^{2} x + 24 e^{2}

y = c_{1} e^{x} + c_{2} x e^{x} + e^{2} x^{3} + 6 e^{2} x^{2} + 18 e^{2} x + 24 e^{2}

y^{^{''}} - 6 y^{^{'}} + 9 y = 18 x + 5

y^{^{''}} - y^{^{'}} - 12 y = e^{2 x} + e^{x - 2}

y^{^{''}} - y^{^{'}} = cos (2 x)

x^{^{''}} + 16 x = sin (4 t)

y^{^{''}} + 3 y^{^{'}} - 4 y = 2 (5 x + 1) e^{x}

What is the solution for (d^2-2d+1)y=x^2e^2x ?
The solution for (d^2-2d+1)y=x^2e^2x is y=c_{1}e^x+c_{2}xe^x+e^2x^3+6e^2x^2+18e^2x+24e^2