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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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