ODE No. 1516

\[ x^3 y^{(3)}(x)+(x+3) x^2 y''(x)+5 (x-6) x y'(x)+(4 x+30) y(x)=0 \] Mathematica : cpu = 261.508 (sec), leaf count = 15142

DSolve[(30 + 4*x)*y[x] + 5*(-6 + x)*x*Derivative[1][y][x] + x^2*(3 + x)*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]
 

\[ \text {Too large to display} \] Maple : cpu = 0.332 (sec), leaf count = 188

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+(x+3)*x^2*diff(diff(y(x),x),x)+5*(x-6)*x*diff(y(x),x)+(4*x+30)*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {c_{3} {\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right ) \Ei \left (1, -x \right )+c_{2} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right ) {\mathrm e}^{-x}+60 c_{3} \left (x^{4}-84 x^{3}+2016 x^{2}-20160 x +75600\right ) \ln \left (x \right )+c_{3} x^{7}+29 c_{3} x^{6}+480 c_{3} x^{5}+\left (c_{1}+5612 c_{3}\right ) x^{4}+\left (-84 c_{1}+40152 c_{3}\right ) x^{3}+\left (2016 c_{1}+654192 c_{3}\right ) x^{2}+\left (-20160 c_{1}-2761920 c_{3}\right ) x +75600 c_{1}+27367200 c_{3}}{x^{6}}\]