Internal problem ID [8602]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1022.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_ellipsoidal]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.181 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x)+(a*cos(2*x)+b)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \MathieuC \left (b , -\frac {a}{2}, x\right )+c_{2} \MathieuS \left (b , -\frac {a}{2}, x\right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 28
DSolve[(b + a*Cos[2*x])*y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ] \\ \end{align*}