Internal problem ID [3284]
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]
\[ \boxed {y^{\prime }+2 y \cot \left (2 x \right )=4 \csc \left (x \right ) x \sec \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 94
dsolve(diff(y(x),x) = 4*csc(x)*x*sec(x)^2-2*y(x)*cot(2*x),y(x), singsol=all)
\[ y \left (x \right ) = 16 \,\operatorname {csgn}\left (\csc \left (2 x \right )\right ) \left (\sqrt {-\frac {{\mathrm e}^{4 i x}}{\left ({\mathrm e}^{4 i x}-1\right )^{2}}}\, \left (i \operatorname {dilog}\left (1+i {\mathrm e}^{i x}\right )-i \operatorname {dilog}\left (1-i {\mathrm e}^{i x}\right )-x \ln \left (1+i {\mathrm e}^{i x}\right )+x \ln \left (1-i {\mathrm e}^{i x}\right )\right )+\frac {\csc \left (2 x \right ) c_{1}}{16}\right ) \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 60
DSolve[y'[x]==2*Csc[x]*2*x*Sec[x]^2-2*y[x]*Cot[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \csc (x) \sec (x) \left (-8 i x \arctan \left (e^{i x}\right )+4 i \operatorname {PolyLog}\left (2,-i e^{i x}\right )-4 i \operatorname {PolyLog}\left (2,i e^{i x}\right )+c_1\right ) \]