Internal problem ID [9681]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1347.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve(diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-1/x^4*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselJ}\left (0, \frac {1}{x}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {1}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 31
DSolve[y''[x] == -(y[x]/x^4) - y'[x]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \operatorname {BesselJ}\left (0,\frac {1}{x}\right )+\frac {c_1 K_0\left (\frac {i}{x}\right )}{\sqrt {\pi }} \]