ODE
\[ x^2 \left (-y'(x)\right )+y''(x)+x y(x)=x \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.208085 (sec), leaf count = 42
\[\left \{\left \{y(x)\to -\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}}+c_1 x+1\right \}\right \}\]
Maple ✓
cpu = 0.181 (sec), leaf count = 53
\[\left [y \left (x \right ) = x \textit {\_C2} +\left (6 \Gamma \left (\frac {2}{3}\right ) 3^{\frac {2}{3}} \left (-x^{3}\right )^{\frac {1}{3}}-6 \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right ) 3^{\frac {2}{3}} \left (-x^{3}\right )^{\frac {1}{3}}+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right ) \textit {\_C1} +1\right ]\] Mathematica raw input
DSolve[x*y[x] - x^2*y'[x] + y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> 1 + x*C[1] - ((-x^3)^(1/3)*C[2]*Gamma[-1/3, -1/3*x^3])/(3*3^(1/3))}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x) = x, y(x))
Maple raw output
[y(x) = x*_C2+(6*GAMMA(2/3)*3^(2/3)*(-x^3)^(1/3)-6*GAMMA(2/3,-1/3*x^3)*3^(2/3)*(-x^3)^(1/3)+18*exp(1/3*x^3))*_C1+1]