60.3.23 problem 1023

Internal problem ID [11019]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1023
Date solved : Thursday, March 13, 2025 at 08:23:24 PM
CAS classification : [_ellipsoidal]

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

✓ Maple. Time used: 0.957 (sec). Leaf size: 29

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

\[ y = c_{1} \operatorname {MathieuC}\left (\frac {a}{2}+b , -\frac {a}{4}, x\right )+c_{2} \operatorname {MathieuS}\left (\frac {a}{2}+b , -\frac {a}{4}, x\right ) \]

✓ Mathematica. Time used: 0.034 (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]
 

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

✗ Sympy

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

False