60.3.22 problem 1022

Internal problem ID [11032]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1022
Date solved : Tuesday, January 28, 2025 at 05:40:30 PM
CAS classification : [_ellipsoidal]

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

✓ Solution by Maple

Time used: 0.995 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 28

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

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