Internal problem ID [9402]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )-\cos \left (x \right )^{2} y=0} \]
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\sin \left (x \right )}+c_{2} {\mathrm e}^{-\sin \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 21
DSolve[-(Cos[x]^2*y[x]) + Tan[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cosh (\sin (x))+i c_2 \sinh (\sin (x)) \]