Internal problem ID [9006]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1429.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {y^{\prime \prime }+\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {y}{\sin \left (x \right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)+1/sin(x)^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\csc \left (x \right )+\cot \left (x \right )\right )+\frac {c_{2}}{\csc \left (x \right )+\cot \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 19
DSolve[y''[x] == Csc[x]^2*y[x] - Cot[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \csc (x) (c_1-i c_2 \cos (x)) \\ \end{align*}