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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = 8 e^{2 t}, y (0) = 1, y^{^{'}} (0) = - 2

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 2 x + 5 - e^{- 2 x}

D (x) = (x - 8)^{2}, S (x) = x^{2} + 2 x + 28

y^{^{''}} + 2 y^{^{'}} = x^{2} + 1

y^{^{''}} - y^{^{'}} - 20 y = 27 e^{- 4 c}

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