ODE No. 1504

\[ \left (x^2+2\right ) y^{(3)}(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0 \]

✓ Mathematica : cpu = 0.406451 (sec), leaf count = 43

DSolve[-2*x*y[x] + (2 + x^2)*Derivative[1][y][x] - 2*x*Derivative[2][y][x] + (2 + x^2)*Derivative[3][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {c_1 x^2}{2}+\frac {1}{2} i c_2 e^{-i x}-\frac {1}{4} c_3 e^{i x}\right \}\right \}\]

✓ Maple : cpu = 0.184 (sec), leaf count = 18

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

\[y \left (x \right ) = c_{1} x^{2}+c_{2} \cos \left (x \right )+c_{3} \sin \left (x \right )\]