Internal problem ID [8649]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1069.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\cot \relax (x ) y^{\prime }+y \left (\sin ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 15
dsolve(diff(diff(y(x),x),x)-diff(y(x),x)*cot(x)+y(x)*sin(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\cos \relax (x )\right )+c_{2} \cos \left (\cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 19
DSolve[Sin[x]^2*y[x] - Cot[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (\cos (x))-c_2 \sin (\cos (x)) \\ \end{align*}