60.3.17 problem 1017

Internal problem ID [11027]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1017
Date solved : Monday, January 27, 2025 at 10:42:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 46

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

\[ y(x)\to c_1 \operatorname {Gamma}(1-v) \operatorname {BesselJ}\left (-v,\sqrt {e^{2 x}}\right )+c_2 \operatorname {Gamma}(v+1) \operatorname {BesselJ}\left (v,\sqrt {e^{2 x}}\right ) \]