60.3.21 problem 1021

Internal problem ID [11031]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1021
Date solved : Tuesday, January 28, 2025 at 05:40:29 PM
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*}

✓ Solution by Maple

Time used: 6.327 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 40

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

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