54.3.21 problem 1021

Internal problem ID [12316]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1021
Date solved : Friday, October 03, 2025 at 03:18:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.108 (sec). Leaf size: 37

ode:=diff(diff(y(x),x),x)+(a*cosh(x)^2+b)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {MathieuC}\left (-\frac {a}{2}-b , \frac {a}{4}, i x \right )+c_2 \operatorname {MathieuS}\left (-\frac {a}{2}-b , \frac {a}{4}, i x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 40

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

\begin{align*} y(x)&\to c_1 \text {MathieuC}\left [\frac {a}{2}+b,-\frac {a}{4},x\right ]+c_2 \text {MathieuS}\left [\frac {a}{2}+b,-\frac {a}{4},x\right ] \end{align*}

✗ Sympy

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

False