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

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

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y^{''}-3y^'+2y=2e^x(1-x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{x} (1 - x)

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

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = 2 e^{x} (1 - x)

Solve linear ODE:

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

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

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