60.3.267 problem 1272

Internal problem ID [11277]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1272
Date solved : Monday, January 27, 2025 at 11:04:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(4*x^2*diff(diff(y(x),x),x)+(4*a^2*x^2+1)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 28

DSolve[(1 + 4*a^2*x^2)*y[x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (c_1 \operatorname {BesselJ}(0,a x)+c_2 \operatorname {BesselY}(0,a x)) \]