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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 t} (cos (t) + 2 sin (t))

y^{^{'''}} + 6 y = 7 y^{^{'}} + 4 e^{x}

y^{^{''}} + y - 12 = 0

x^{^{''}} - 3 x^{^{'}} + 2 x = 20 sin (2 t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 8 e^{6 x}

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