60.3.336 problem 1342

Internal problem ID [11346]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1342
Date solved : Monday, January 27, 2025 at 11:17:32 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 31

dsolve(diff(diff(y(x),x),x) = -a/x^4*y(x),y(x), singsol=all)
 

\[ y = x \left (c_{1} \sinh \left (\frac {\sqrt {-a}}{x}\right )+c_{2} \cosh \left (\frac {\sqrt {-a}}{x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 56

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

\[ y(x)\to c_1 x e^{-1+\frac {i \sqrt {a}}{x}}-\frac {i c_2 x e^{1-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}} \]