Internal problem ID [9011]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1432.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {\cos \relax (x ) y^{\prime }}{\sin \relax (x )}+\frac {\left (-17 \left (\sin ^{2}\relax (x )\right )-1\right ) y}{4 \sin \relax (x )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)-1/4*(-17*sin(x)^2-1)/sin(x)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sinh \left (2 x \right )}{\sqrt {\sin \relax (x )}}+\frac {c_{2} \cosh \left (2 x \right )}{\sqrt {\sin \relax (x )}} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 33
DSolve[y''[x] == -1/4*(Csc[x]^2*(-1 - 17*Sin[x]^2)*y[x]) - Cot[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-2 x} \left (c_2 e^{4 x}+4 c_1\right )}{4 \sqrt {\sin (x)}} \\ \end{align*}