What is the solution for x^2y^{''}-8x^2y^'+16x^2y=3e^{4x} ?

The solution for x^2y^{''}-8x^2y^'+16x^2y=3e^{4x} is y=c_{1}e^{4x}+c_{2}xe^{4x}-3e^{4x}ln(x)-3e^{4x}

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x^2y^{''}-8x^2y^'+16x^2y=3e^{4x}

x^{2} y^{^{''}} - 8 x^{2} y^{^{'}} + 16 x^{2} y = 3 e^{4 x}

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

Solution steps

x^{2} y^{''} (x) - 8 x^{2} y^{'} (x) + 16 x^{2} y = 3 e^{4 x}

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 e^{t}, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 x^{2} + 5

y^{^{''}} - y^{^{'}} - 6 y = 73 cos (3 x)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 8 t

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 7 t

What is the solution for x^2y^{''}-8x^2y^'+16x^2y=3e^{4x} ?
The solution for x^2y^{''}-8x^2y^'+16x^2y=3e^{4x} is y=c_{1}e^{4x}+c_{2}xe^{4x}-3e^{4x}ln(x)-3e^{4x}