Internal problem ID [9841]
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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 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), singsol=all)
\[ y \left (x \right ) = \frac {c_{3} {\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right ) \operatorname {expIntegral}_{1}\left (-x \right )+c_{2} {\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right )+60 c_{3} \left (x^{4}-84 x^{3}+2016 x^{2}-20160 x +75600\right ) \ln \left (x \right )+c_{3} x^{7}+29 c_{3} x^{6}+480 x^{5} c_{3} +\left (c_{1} +5612 c_{3} \right ) x^{4}+\left (-84 c_{1} +40152 c_{3} \right ) x^{3}+\left (2016 c_{1} +654192 c_{3} \right ) x^{2}+\left (-20160 c_{1} -2761920 c_{3} \right ) x +75600 c_{1} +27367200 c_{3}}{x^{6}} \]
✗ 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