What is the solution for y^{''}-6y^'+5y=9e^{2x} ?

The solution for y^{''}-6y^'+5y=9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x-3e^{2x}

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y^{''}-6y^'+5y=9e^{2x}

y^{^{''}} - 6 y^{^{'}} + 5 y = 9 e^{2 x}

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

Solution steps

y^{''} (x) - 6 y^{'} (x) + 5 y = 9 e^{2 x}

Solve linear ODE:

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

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

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

y^{^{'''}} - 7 y^{^{'}} - 6 y = 26 e^{2 x}

(d^{3} - 3 d^{2} + 4) y = e^{2 x}

\frac{d ^{2} y}{d t ^{2}} + 9 y = cos (3 t)

y^{^{''}} + 9 y = cos (2 t), y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}-6y^'+5y=9e^{2x} ?
The solution for y^{''}-6y^'+5y=9e^{2x} is y=c_{1}e^{5x}+c_{2}e^x-3e^{2x}