What is the solution for y^{''}+5y^'-6y=10e^{2x} ?

The solution for y^{''}+5y^'-6y=10e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}+5/4 e^{2x}

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y^{''}+5y^'-6y=10e^{2x}

y^{^{''}} + 5 y^{^{'}} - 6 y = 10 e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{5}{4} e^{2 x}

Solution steps

y^{''} (x) + 5 y^{'} (x) - 6 y = 10 e^{2 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{5}{4} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- 6 x} + \frac{5}{4} e^{2 x}

y^{^{''}} + 4 y = 9 sin (t)

y^{^{''''}} - y = 6 t + cos (t)

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

y^{^{''}} - 6 y^{^{'}} + 13 y = 4 e^{3 x}, y (0) = 2, y^{^{'}} (0) = 4

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

What is the solution for y^{''}+5y^'-6y=10e^{2x} ?
The solution for y^{''}+5y^'-6y=10e^{2x} is y=c_{1}e^x+c_{2}e^{-6x}+5/4 e^{2x}