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 = 0.00684482 (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 = 0.106 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =x \left ( {{\sl U}\left ({\frac {1}{2}}-{\frac {n}{2}},\,{\frac {3}{2}},\,{x}^{2}\right )}{\it \_C2}+{{\sl M}\left ({\frac {1}{2}}-{\frac {n}{2}},\,{\frac {3}{2}},\,{x}^{2}\right )}{\it \_C1} \right ) \right \} \] 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[-n/2, 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),'implicit')
Maple raw output
y(x) = x*(KummerU(1/2-1/2*n,3/2,x^2)*_C2+KummerM(1/2-1/2*n,3/2,x^2)*_C1)