Internal problem ID [6705]
Book: Second order enumerated odes
Section: section 2
Problem number: 21.
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)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\cot \relax (x ) y^{\prime }+4 y \left (\csc ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+cot(x)*diff(y(x),x)+4*y(x)*csc(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\csc \relax (x )-\cot \relax (x )\right )^{2 i}+c_{2} \left (\csc \relax (x )-\cot \relax (x )\right )^{-2 i} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 53
DSolve[y''[x]+Cot[x]*y'[x]+4*y[x]*Csc[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (2 \left (\log \left (\cos \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )\right )\right )\right )-c_2 \sin \left (2 \left (\log \left (\cos \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )\right )\right )\right ) \\ \end{align*}