What is the solution for y^{''}-3y^'-10y=2e^{3x} ?

The solution for y^{''}-3y^'-10y=2e^{3x} is y=c_{1}e^{5x}+c_{2}e^{-2x}-1/5 e^{3x}

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y^{''}-3y^'-10y=2e^{3x}

y^{^{''}} - 3 y^{^{'}} - 10 y = 2 e^{3 x}

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

Solution steps

y^{''} (x) - 3 y^{'} (x) - 10 y = 2 e^{3 x}

Solve linear ODE:

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

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

y^{^{''}} - 4 y = \frac{( e ^{2 x} )}{x}

5 y^{^{''}} + 180 y = 90 sin (6 t)

y^{^{''}} + 2 y^{^{'}} - 2 y = 8 e^{- 3 x}

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

y^{^{''}} - y^{^{'}} - 6 y = 12 x - e^{x}, y (0) = 1

What is the solution for y^{''}-3y^'-10y=2e^{3x} ?
The solution for y^{''}-3y^'-10y=2e^{3x} is y=c_{1}e^{5x}+c_{2}e^{-2x}-1/5 e^{3x}