Internal problem ID [9083]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1504.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime }-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 18
dsolve((x^2+2)*diff(diff(diff(y(x),x),x),x)-2*x*diff(diff(y(x),x),x)+(x^2+2)*diff(y(x),x)-2*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+c_{2} \cos \relax (x )+c_{3} \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 41
DSolve[-2*x*y[x] + (2 + x^2)*y'[x] - 2*x*y''[x] + (2 + x^2)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (2 c_1 x^2-c_3 e^{i x}+2 c_2 (\sin (x)+i \cos (x))\right ) \\ \end{align*}