4.21   ODE No. 1021

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a{(\cosh \left(x\right))}^2+b)y\left(x\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.053507 (sec), leaf count = 44 $$\left\{\{y(x)\to c_1\text{MathieuC}[\frac{1}{2}(a+2b),-\frac{a}{4},x]+c_2\text{MathieuS}[\frac{1}{2}(a+2b),-\frac{a}{4},x]\}\right\}$$

Maple: cpu = 0.140 (sec), leaf count = 39 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{C}(-\frac{a}{2}-b,\frac{a}{4},ix)+\mathit{\_}\mathit{C}\mathit{2}\mathit{M}\mathit{a}\mathit{t}\mathit{h}\mathit{i}\mathit{e}\mathit{u}\mathit{S}(-\frac{a}{2}-b,\frac{a}{4},ix)\}$$