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

\int \frac{5 x}{9 x ^{2} - 4} d x

n = 0 \sum \infty e^{\frac{- n}{2}}

(x + y) d x + (x) d y = 0

\int (2 - sin (\frac{t}{4}))^{2} cos (\frac{t}{4}) d t

\frac{d y}{d x} = (cos (2 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