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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

\int (8 x - 4) d x

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

\int_{0}^{0} x d x

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