Internal problem ID [3364]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 624.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\left (\cot \relax (x )-2 y^{2}\right ) y^{\prime }-y^{3} \csc \relax (x ) \sec \relax (x )=0} \end {gather*}
✗ Solution by Maple
dsolve((cot(x)-2*y(x)^2)*diff(y(x),x) = y(x)^3*csc(x)*sec(x),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 60.366 (sec). Leaf size: 69
DSolve[(Cot[x]-2 y[x]^2)y'[x]==y[x]^3 Csc[x] Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {\cot (x)} \sqrt {\text {ProductLog}\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}} \\ y(x)\to \frac {i \sqrt {\cot (x)} \sqrt {\text {ProductLog}\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}} \\ \end{align*}