60.3.269 problem 1274

Internal problem ID [11279]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1274
Date solved : Monday, January 27, 2025 at 11:04:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 38

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

\[ y(x)\to c_1 \operatorname {Gamma}(1-v) \operatorname {BesselJ}\left (-v,\sqrt {x}\right )+c_2 \operatorname {Gamma}(v+1) \operatorname {BesselJ}\left (v,\sqrt {x}\right ) \]