What is the solution for y^{''}-5y^'+6y=xe^{2x} ?

The solution for y^{''}-5y^'+6y=xe^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-(e^{2x}x^2)/2-e^{2x}x

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y^{''}-5y^'+6y=xe^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = x e^{2 x}

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = x e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 2 y = 4 - 2 x

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

x^{^{''}} + 2 x^{^{'}} + x = t^{2} e^{2 t}

y^{^{''}} + y = x, y (π) = 0, y (0) = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 4 e^{6 x}

What is the solution for y^{''}-5y^'+6y=xe^{2x} ?
The solution for y^{''}-5y^'+6y=xe^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-(e^{2x}x^2)/2-e^{2x}x