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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y = e^{t} + e^{- t}

3 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 = 0

y^{^{''}} + 3 y = cos (x)

y^{^{''}} + 25 y = 2 x \cdot cos (5 x)

y^{^{''''}} + 2 y^{^{''}} + y = cos (3 x) + 5

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