What is the solution for y^{''}-y^'=4e^{-x}+3e^{2x} ?

The solution for y^{''}-y^'=4e^{-x}+3e^{2x} is y=c_{1}e^x+c_{2}+2e^{-x}+3/2 e^{2x}

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y^{''}-y^'=4e^{-x}+3e^{2x}

y^{^{''}} - y^{^{'}} = 4 e^{- x} + 3 e^{2 x}

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y = 4 sin (3 t)

0.25 y^{^{''}} + 0.25 y^{^{'}} + 16 y = 5 cos (2 t)

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

y^{^{''}} + 9 y = sin (2.9 t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = 11 sec^{2} (2 t)

What is the solution for y^{''}-y^'=4e^{-x}+3e^{2x} ?
The solution for y^{''}-y^'=4e^{-x}+3e^{2x} is y=c_{1}e^x+c_{2}+2e^{-x}+3/2 e^{2x}