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

The solution for y^{''}-2y^'-3y=2ex-10 is y=c_{1}e^{3x}+c_{2}e^{-x}-(2ex)/3+(4e+30)/9

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y^{''}-2y^'-3y=2ex-10

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

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{2 e x}{3} + \frac{4 e + 30}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{2 e x}{3} + \frac{4 e + 30}{9}

y = c_{1} e^{3 x} + c_{2} e^{- x} - \frac{2 e x}{3} + \frac{4 e + 30}{9}

What is the solution for y^{''}-2y^'-3y=2ex-10 ?
The solution for y^{''}-2y^'-3y=2ex-10 is y=c_{1}e^{3x}+c_{2}e^{-x}-(2ex)/3+(4e+30)/9