Internal problem ID [8647]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1067.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\tan \relax (x ) y^{\prime }-\left (\cos ^{2}\relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(diff(y(x),x),x)+diff(y(x),x)*tan(x)-y(x)*cos(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\sin \relax (x )}+c_{2} {\mathrm e}^{-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 21
DSolve[-(Cos[x]^2*y[x]) + Tan[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh (\sin (x))+i c_2 \sinh (\sin (x)) \\ \end{align*}