ODE No. 1058

\[ \left (x^4-2\right ) x y(x)-\left ((x+1) x^2 y'(x)\right )+y''(x)=0 \] Mathematica : cpu = 0.0527202 (sec), leaf count = 56

DSolve[x*(-2 + x^4)*y[x] - x^2*(1 + x)*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 e^{\frac {x^3}{3}} \int _1^xe^{\frac {K[1]^4}{4}-\frac {K[1]^3}{3}}dK[1]+c_1 e^{\frac {x^3}{3}}\right \}\right \}\] Maple : cpu = 0.122 (sec), leaf count = 29

dsolve(diff(diff(y(x),x),x)-x^2*(1+x)*diff(y(x),x)+x*(x^4-2)*y(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\frac {x^{3}}{3}} \left (\left (\int {\mathrm e}^{\frac {1}{4} x^{4}-\frac {1}{3} x^{3}}d x \right ) c_{2}+c_{1}\right )\]