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

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

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y^{''}-7y^'+12y=4e^{2x}

y^{^{''}} - 7 y^{^{'}} + 12 y = 4 e^{2 x}

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

Solution steps

y^{''} (x) - 7 y^{'} (x) + 12 y = 4 e^{2 x}

Solve linear ODE:

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

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

y^{^{''}} - 49 y = cosh (7 x)

y^{^{''}} + y = 2 cos^{2} (x)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 9 + e^{\frac{x}{2}}

4 y^{^{''}} + y + 2 = 0, y (0) = 0, y^{^{'}} (0) = \frac{1}{2}

y^{^{''}} + 4 y = 9 sec (2 x)

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