What is the solution for y^{''}-5y^'+6y=4xe^{2x} ?

The solution for y^{''}-5y^'+6y=4xe^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-2x^2e^{2x}-4e^{2x}x

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y^{''}-5y^'+6y=4xe^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 4 x e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 2 x^{2} e^{2 x} - 4 e^{2 x} x

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 4 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 2 x^{2} e^{2 x} - 4 e^{2 x} x

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 2 x^{2} e^{2 x} - 4 e^{2 x} x

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

y^{^{''}} - 9 y = sinh (3 x)

y^{^{''''}} - 2 y^{^{'''}} + y^{^{''}} = e^{x} + 1

y^{^{''}} + 6 y^{^{'}} - 7 y = 3 e^{2 x} - e^{- x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = tan (x)

What is the solution for y^{''}-5y^'+6y=4xe^{2x} ?
The solution for y^{''}-5y^'+6y=4xe^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-2x^2e^{2x}-4e^{2x}x