What is the solution for y^{''}-6y^'+8y=e^x(11-6x) ?

The solution for y^{''}-6y^'+8y=e^x(11-6x) is y=c_{1}e^{4x}+c_{2}e^{2x}-2xe^x+e^x

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y^{''}-6y^'+8y=e^x(11-6x)

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{x} (11 - 6 x)

y = c_{1} e^{4 x} + c_{2} e^{2 x} - 2 x e^{x} + e^{x}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = e^{x} (11 - 6 x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} - 2 x e^{x} + e^{x}

y = c_{1} e^{4 x} + c_{2} e^{2 x} - 2 x e^{x} + e^{x}

\frac{3 s + 5}{s ^{2} + 4 s + 13}

\int \frac{e ^{x}}{3 + 2 e ^{x} - e ^{2 x}} d x

y = 9 x^{2} - x^{3} + x, y = x^{2} + 16 x

x \to 3 lim (\frac{x ^{2} - 1}{x - 1})

\frac{d}{d x} (e^{x} (x - 7))

What is the solution for y^{''}-6y^'+8y=e^x(11-6x) ?
The solution for y^{''}-6y^'+8y=e^x(11-6x) is y=c_{1}e^{4x}+c_{2}e^{2x}-2xe^x+e^x