Internal problem ID [9827]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1500.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 114
dsolve(x^2*diff(diff(diff(y(x),x),x),x)-(x+nu)*x*diff(diff(y(x),x),x)+nu*(2*x+1)*diff(y(x),x)-nu*(x+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-c_{3} x^{\frac {\nu }{2}+1} \operatorname {BesselY}\left (-\nu +1, 2 \sqrt {\nu }\, \sqrt {x}\right )-c_{2} x^{\frac {\nu }{2}+1} \operatorname {BesselJ}\left (-\nu +1, 2 \sqrt {\nu }\, \sqrt {x}\right )-x^{\frac {\nu }{2}+\frac {1}{2}} \sqrt {\nu }\, \operatorname {BesselY}\left (-\nu , 2 \sqrt {\nu }\, \sqrt {x}\right ) c_{3} -x^{\frac {\nu }{2}+\frac {1}{2}} \sqrt {\nu }\, \operatorname {BesselJ}\left (-\nu , 2 \sqrt {\nu }\, \sqrt {x}\right ) c_{2} +c_{1} {\mathrm e}^{x} \sqrt {x}}{\sqrt {x}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(nu*(1 + x)*y[x]) + nu*(1 + 2*x)*y'[x] - x*(v + x)*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved