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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

y^{^{''}} + 9 y = - 24 sin (3 t)

x \to - 3 lim (x^{2} + 2 x - 3)

\int (x + 3) x + 3 d x

9 y^{^{''}} + 30 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 1

\frac{\partial}{\partial r} (r cos (s))

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