Internal problem ID [9074]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1495.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }+6 y^{\prime \prime } x +6 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x)+6*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\frac {c_{2}}{x}+\frac {c_{3}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 23
DSolve[6*y'[x] + 6*x*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3-\frac {2 c_2 x+c_1}{2 x^2} \\ \end{align*}