Internal problem ID [2775]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-4 \csc \relax (x ) x \left (\sec ^{2}\relax (x )\right )+2 y \cot \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 98
dsolve(diff(y(x),x) = 4*csc(x)*x*sec(x)^2-2*y(x)*cot(2*x),y(x), singsol=all)
\[ y \relax (x ) = \left (-32 \sqrt {-\frac {{\mathrm e}^{4 i x}}{\left ({\mathrm e}^{4 i x}-1\right )^{2}}}\, \left (\frac {x \ln \left (1+i {\mathrm e}^{i x}\right )}{2}-\frac {x \ln \left (1-i {\mathrm e}^{i x}\right )}{2}-\frac {i \dilog \left (1+i {\mathrm e}^{i x}\right )}{2}+\frac {i \dilog \left (1-i {\mathrm e}^{i x}\right )}{2}\right ) \sin \left (2 x \right )+c_{1}\right ) \sqrt {\cot ^{2}\left (2 x \right )+1} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 58
DSolve[y'[x]==2*Csc[x]*2*x*Sec[x]^2-2*y[x]*Cot[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \csc (x) \sec (x) \left (-4 i \text {PolyLog}\left (2,i e^{i x}\right )+4 i \text {PolyLog}(2,\sin (x)-i \cos (x))-8 i x \text {ArcTan}\left (e^{i x}\right )+c_1\right ) \\ \end{align*}