\[ -\left (4 x^2+2\right ) x^2 y''(x)+\left (10 x^2+4\right ) x y'(x)-4 \left (3 x^2+1\right ) y(x)+\left (x^2+1\right ) x^3 y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.275438 (sec), leaf count = 74
DSolve[-4*(1 + 3*x^2)*y[x] + x*(4 + 10*x^2)*Derivative[1][y][x] - x^2*(2 + 4*x^2)*Derivative[2][y][x] + x^3*(1 + x^2)*Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \left (-x^3+3 x^2-x\right )+\frac {1}{2} c_2 \left (x^3-2 x^2+x\right )-\frac {c_3 x \left (-x^3+3 x^2-x\right ) (\log (x)+1)}{2 \left (x^2-3 x+1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.311 (sec), leaf count = 23
dsolve((x^2+1)*x^3*diff(diff(diff(y(x),x),x),x)-(4*x^2+2)*x^2*diff(diff(y(x),x),x)+(10*x^2+4)*x*diff(y(x),x)-4*(3*x^2+1)*y(x)=0,y(x))
\[y \left (x \right ) = \left (\ln \left (x \right ) c_{2} x +c_{3} x^{2}+\left (c_{1}+c_{2}\right ) x +c_{3}\right ) x\]