Internal problem ID [9069]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1490.
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 }-y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 18
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-x*diff(diff(y(x),x),x)+(x^2+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x \BesselJ \left (1, x\right )+c_{3} x \BesselY \left (1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 22
DSolve[(1 + x^2)*y'[x] - x*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x J_1(x)+c_2 x Y_1(x)+c_3 \\ \end{align*}