What is the solution for y^{''}-7y^'+12y=e^{3x}+e^{4x} ?

The solution for y^{''}-7y^'+12y=e^{3x}+e^{4x} is y=c_{1}e^{4x}+c_{2}e^{3x}-e^{3x}x+e^{4x}x

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y^{''}-7y^'+12y=e^{3x}+e^{4x}

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{3 x} + e^{4 x}

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

Solution steps

y^{''} (x) - 7 y^{'} (x) + 12 y = e^{3 x} + e^{4 x}

Solve linear ODE:

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

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

y^{^{''}} + 9 y = e^{- 2 t}

y^{^{''}} + 6 y^{^{'}} + 73 y = 80 e^{x} cos (4 x)

y^{^{''}} + 2 y^{^{'}} + y = 15 e^{- x} x + 1

y^{^{''}} + 4 y = 13 sec^{2} (2 t)

y^{^{''}} + y^{^{'}} = 3 + e^{x}

What is the solution for y^{''}-7y^'+12y=e^{3x}+e^{4x} ?
The solution for y^{''}-7y^'+12y=e^{3x}+e^{4x} is y=c_{1}e^{4x}+c_{2}e^{3x}-e^{3x}x+e^{4x}x