ODE
\[ 2 n y(x)+y''(x)-2 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.153003 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_1 H_n(x)+c_2 \, _1F_1\left (-\frac {n}{2};\frac {1}{2};x^2\right )\right \}\right \}\]
Maple ✓
cpu = 0.409 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} \KummerM \left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, x^{2}\right ) x +\textit {\_C2} \KummerU \left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, x^{2}\right ) x\right ]\] Mathematica raw input
DSolve[2*n*y[x] - 2*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*HermiteH[n, x] + C[2]*Hypergeometric1F1[-1/2*n, 1/2, x^2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*n*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*KummerM(1/2-1/2*n,3/2,x^2)*x+_C2*KummerU(1/2-1/2*n,3/2,x^2)*x]