60.3.17 problem 1017

Internal problem ID [11013]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1017
Date solved : Sunday, March 30, 2025 at 07:39:07 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*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 17

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

\[ y = c_1 \operatorname {BesselJ}\left (v , {\mathrm e}^{x}\right )+c_2 \operatorname {BesselY}\left (v , {\mathrm e}^{x}\right ) \]

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

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
v = symbols("v") 
y = Function("y") 
ode = Eq((-v**2 + exp(2*x))*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False