60.3.341 problem 1347

Internal problem ID [11351]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1347
Date solved : Monday, January 27, 2025 at 11:17:41 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x}-\frac {y}{x^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.059 (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)
 

\[ y = c_{1} \operatorname {BesselJ}\left (0, \frac {1}{x}\right )+c_{2} \operatorname {BesselY}\left (0, \frac {1}{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}] == -(y[x]/x^4) - D[y[x],x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \operatorname {BesselJ}\left (0,\frac {1}{x}\right )+\frac {c_1 K_0\left (\frac {i}{x}\right )}{\sqrt {\pi }} \]