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

The solution for x^3y^{'''}-x^2y^{''}+2xy^'-2y=x^3 is y=c_{1}x^2+c_{2}x+c_{3}ln(x)x+(x^3)/4

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

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

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{x ^{3}}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{x ^{3}}{4}

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{x ^{3}}{4}

\int \frac{1}{x ^{2} + \frac{3}{4}} d x

\frac{1}{x ^{2} + 3}

f (x) = - x^{3}, (- 1, 1)

\int_{- 2}^{1} 2 x d x

\frac{d y}{d x} = 5 x y

What is the solution for x^3y^{'''}-x^2y^{''}+2xy^'-2y=x^3 ?
The solution for x^3y^{'''}-x^2y^{''}+2xy^'-2y=x^3 is y=c_{1}x^2+c_{2}x+c_{3}ln(x)x+(x^3)/4