Internal problem ID [2777]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 22.
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 (\sin ^{3}\relax (x )+y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 116
dsolve(diff(y(x),x) = 4*csc(x)*x*(sin(x)^3+y(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (1+{\mathrm e}^{i x}\right )^{-4 x} \left (1-{\mathrm e}^{i x}\right )^{4 x} {\mathrm e}^{4 i \left (\dilog \left (1+{\mathrm e}^{i x}\right )-\dilog \left (1-{\mathrm e}^{i x}\right )\right )} \left (c_{1}+\int -2 x \left (1-{\mathrm e}^{i x}\right )^{-4 x} \left (1+{\mathrm e}^{i x}\right )^{4 x} {\mathrm e}^{-4 i \left (\dilog \left (1+{\mathrm e}^{i x}\right )-\dilog \left (1-{\mathrm e}^{i x}\right )\right )} \left (-1+\cos \left (2 x \right )\right )d x \right ) \]
✓ Solution by Mathematica
Time used: 1.121 (sec). Leaf size: 109
DSolve[y'[x]==2*Csc[x]*2*x(Sin[x]^3+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-8 i \text {PolyLog}\left (2,e^{i x}\right )+2 i \text {PolyLog}\left (2,e^{2 i x}\right )-8 x \tanh ^{-1}\left (e^{i x}\right )\right ) \left (\int _1^x4 \exp \left (8 \tanh ^{-1}\left (e^{i K[1]}\right ) K[1]+8 i \text {PolyLog}\left (2,e^{i K[1]}\right )-2 i \text {PolyLog}\left (2,e^{2 i K[1]}\right )\right ) K[1] \sin ^2(K[1])dK[1]+c_1\right ) \\ \end{align*}