What is the solution for y^{''}-y^'-2y=7e^{2x}-3e^x ?

The solution for y^{''}-y^'-2y=7e^{2x}-3e^x is y=c_{1}e^{2x}+c_{2}e^{-x}+(7e^{2x}x)/3+3/2 e^x

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y^{''}-y^'-2y=7e^{2x}-3e^x

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{2 x} - 3 e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{7 e ^{2 x} x}{3} + \frac{3}{2} e^{x}

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 7 e^{2 x} - 3 e^{x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{7 e ^{2 x} x}{3} + \frac{3}{2} e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{7 e ^{2 x} x}{3} + \frac{3}{2} e^{x}

What is the solution for y^{''}-y^'-2y=7e^{2x}-3e^x ?
The solution for y^{''}-y^'-2y=7e^{2x}-3e^x is y=c_{1}e^{2x}+c_{2}e^{-x}+(7e^{2x}x)/3+3/2 e^x