ODE No. 1513

\[ x^3 y^{(3)}(x)-4 x^2 y''(x)+\left (x^2+8\right ) x y'(x)-2 \left (x^2+4\right ) y(x)=0 \]

✓ Mathematica : cpu = 0.121711 (sec), leaf count = 25

DSolve[-2*(4 + x^2)*y[x] + x*(8 + x^2)*Derivative[1][y][x] - 4*x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_1 x^2+c_3 x \cos (x)-c_2 x \sin (x)\right \}\right \}\]

✓ Maple : cpu = 0.177 (sec), leaf count = 18

dsolve(x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+(x^2+8)*x*diff(y(x),x)-2*(x^2+4)*y(x)=0,y(x))

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