ODE
\[ -\left (2 x^2+1\right ) y'(x)+2 x y''(x)-x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.206172 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {1}{2} e^{\frac {x^2}{2}} \left (2 c_1-\frac {2^{3/4} c_2 \sqrt [4]{x^2} \Gamma \left (\frac {3}{4},\frac {x^2}{2}\right )}{\sqrt {x}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.449 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} \KummerM \left (1, \frac {7}{4}, \frac {x^{2}}{2}\right ) x^{\frac {3}{2}}+\textit {\_C2} \KummerU \left (1, \frac {7}{4}, \frac {x^{2}}{2}\right ) x^{\frac {3}{2}}\right ]\] Mathematica raw input
DSolve[-(x*y[x]) - (1 + 2*x^2)*y'[x] + 2*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(x^2/2)*(2*C[1] - (2^(3/4)*(x^2)^(1/4)*C[2]*Gamma[3/4, x^2/2])/Sqrt[x]))/2}}
Maple raw input
dsolve(2*x*diff(diff(y(x),x),x)-(2*x^2+1)*diff(y(x),x)-x*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*KummerM(1,7/4,1/2*x^2)*x^(3/2)+_C2*KummerU(1,7/4,1/2*x^2)*x^(3/2)]