Internal problem ID [8646]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1066.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } \tan \relax (x )+y \left (\cos ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 15
dsolve(diff(diff(y(x),x),x)+diff(y(x),x)*tan(x)+y(x)*cos(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sin \relax (x )\right )+c_{2} \cos \left (\sin \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 18
DSolve[Cos[x]^2*y[x] + Tan[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sin (\sin (x))+c_1 \cos (\sin (x)) \\ \end{align*}