60.3.22 problem 1022

Internal problem ID [11018]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1022
Date solved : Sunday, March 30, 2025 at 07:39:14 PM
CAS classification : [_ellipsoidal]

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

✓ Maple. Time used: 0.111 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 28

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

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

✗ Sympy

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

False