Internal problem ID [9750]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1422.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\frac {2 y}{\sin \left (x \right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 31
dsolve(diff(diff(y(x),x),x) = 2/sin(x)^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -i \cot \left (x \right ) \ln \left (\cos \left (2 x \right )+i \sin \left (2 x \right )\right ) c_{2} +c_{1} \cot \left (x \right )-2 c_{2} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 46
DSolve[y''[x] == 2*Csc[x]^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\cos (x) \left (c_1-c_2 \log \left (\sqrt {-\sin ^2(x)}-\cos (x)\right )\right )}{\sqrt {-\sin ^2(x)}}-c_2 \]