Internal problem ID [9095]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1516.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime } x^{3}+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 263
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), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{4}-84 x^{3}+2016 x^{2}-20160 x +75600\right )}{x^{6}}+\frac {c_{2} {\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right )}{x^{6}}+\frac {c_{3} \left ({\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{8}+28 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{7}+450 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{6}+5100 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{5}+x^{7}+42900 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{4}+29 x^{6}+267120 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right ) x^{3}+60 x^{4} \ln \relax (x )+480 x^{5}+1179360 \,{\mathrm e}^{-x} x^{2} \expIntegral \left (1, -x \right )-5040 \ln \relax (x ) x^{3}+5612 x^{4}+3326400 \,{\mathrm e}^{-x} x \expIntegral \left (1, -x \right )+120960 x^{2} \ln \relax (x )+40152 x^{3}+4536000 \,{\mathrm e}^{-x} \expIntegral \left (1, -x \right )-1209600 x \ln \relax (x )+654192 x^{2}+4536000 \ln \relax (x )-2761920 x +27367200\right )}{x^{6}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(30 + 4*x)*y[x] + 5*(-6 + x)*x*y'[x] + x^2*(3 + x)*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Timed out