Internal problem ID [9056]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1477.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 41
dsolve(x*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 43
DSolve[x*y[x] + 3*y''[x] + x*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 e^{-x}+c_2 e^{\sqrt [3]{-1} x}+c_3 e^{-(-1)^{2/3} x}}{x} \\ \end{align*}