What is the solution for y^{''}-2y^'+y=e^x(2-12x) ?

The solution for y^{''}-2y^'+y=e^x(2-12x) is y=c_{1}e^x+c_{2}xe^x-2x^3e^x+e^xx^2

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

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

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{3} e^{x} + e^{x} x^{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{3} e^{x} + e^{x} x^{2}

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{3} e^{x} + e^{x} x^{2}

\int \frac{e ^{x}}{e ^{2 x} + 9} d x

y = 5 x^{2} - 12 x - \frac{8}{x ^{2}}

- \frac{1}{2 x ^{\frac{3}{2}}}

\int 2 tanh (x) d x

ln (7)

What is the solution for y^{''}-2y^'+y=e^x(2-12x) ?
The solution for y^{''}-2y^'+y=e^x(2-12x) is y=c_{1}e^x+c_{2}xe^x-2x^3e^x+e^xx^2