ODE
\[ \left (x^2+1\right ) y''(x)-4 x y'(x)+6 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0522044 (sec), leaf count = 33
\[\left \{\left \{y(x)\to -\frac {1}{3} i \left (c_2 \left (3 x^2-1\right )+3 c_1 (x-i)^3\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{x}^{3}-3\,{\it \_C1}\,{x}^{2}-3\,{\it \_C2}\,x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[6*y[x] - 4*x*y'[x] + (1 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-I/3)*(3*(-I + x)^3*C[1] + (-1 + 3*x^2)*C[2])}}
Maple raw input
dsolve((x^2+1)*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*x^3-3*_C1*x^2-3*_C2*x+_C1