29.22.16 problem 624

Internal problem ID [5216]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 624
Date solved : Monday, January 27, 2025 at 10:21:51 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime }&=y^{3} \csc \left (x \right ) \sec \left (x \right ) \end{align*}

✗ 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: 4.744 (sec). Leaf size: 74

DSolve[(Cot[x]-2 y[x]^2)D[y[x],x]==y[x]^3 Csc[x] Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}} \\ y(x)\to \frac {i \sqrt {\cot (x)} \sqrt {W\left (-2 e^{-8 c_1} \tan (x)\right )}}{\sqrt {2}} \\ y(x)\to 0 \\ \end{align*}