Internal problem ID [9067]
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]]
\[ \boxed {x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime } \left (x^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{1} +c_{2} x \operatorname {BesselJ}\left (1, x\right )+c_{3} x \operatorname {BesselY}\left (1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (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 \operatorname {BesselJ}(1,x)+c_2 x Y_1(x)+c_3 \\ \end{align*}