What is the solution for y^{''}-5y^'+6y=5e^{2x} ?

The solution for y^{''}-5y^'+6y=5e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-5xe^{2x}

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y^{''}-5y^'+6y=5e^{2x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 5 e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 5 x e^{2 x}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = 5 e^{2 x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 5 x e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{2 x} - 5 x e^{2 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 t}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 0 + 6 sin (x)

y^{^{''}} + y = 2 sin (2 t)

y^{^{''}} + y = sin (x), y^{^{'}} (\frac{π}{2}) = \frac{3}{2}, y (0) = 0

y^{^{''}} - 4 y^{^{'}} + 5 y = 125 t^{2}

What is the solution for y^{''}-5y^'+6y=5e^{2x} ?
The solution for y^{''}-5y^'+6y=5e^{2x} is y=c_{1}e^{3x}+c_{2}e^{2x}-5xe^{2x}