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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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