What is the solution for y^{''}-4y^'+4y=(12x^2-6x)e^{2x} ?

The solution for y^{''}-4y^'+4y=(12x^2-6x)e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+e^{2x}x^4-e^{2x}x^3

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y^{''}-4y^'+4y=(12x^2-6x)e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = (12 x^{2} - 6 x) e^{2 x}

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = (12 x^{2} - 6 x) e^{2 x}

Solve linear ODE:

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

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

\int \frac{( 12 x + 30 )}{x ^{2} + 2 x - 8} d x

\int_{1}^{2} \frac{4 y ^{2} - 6 y - 12}{y ( y + 2 ) ( y - 3 )} d y

\int x^{2} sinh (x) d x

f (x) = 2 x^{- 2} - 3 x^{- \frac{7}{3}}

\int 3 x x - 5 d x

What is the solution for y^{''}-4y^'+4y=(12x^2-6x)e^{2x} ?
The solution for y^{''}-4y^'+4y=(12x^2-6x)e^{2x} is y=c_{1}e^{2x}+c_{2}xe^{2x}+e^{2x}x^4-e^{2x}x^3