29.5.1 problem 116

Internal problem ID [4718]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 116
Date solved : Tuesday, March 04, 2025 at 07:10:23 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.239 (sec). Leaf size: 14

ode:=diff(y(x),x) = sin(x)*(csc(y(x))-cot(y(x))); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \arccos \left (c_{1} {\mathrm e}^{-\cos \left (x \right )}+1\right ) \]

✓ Mathematica. Time used: 0.419 (sec). Leaf size: 70

ode=D[y[x],x]==Sin[x](Csc[y[x]]-Cot[y[x]]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \cos (x) \tan \left (\frac {y(x)}{2}\right ) e^{\text {arctanh}(\cos (y(x)))}-\sqrt {\sin ^2(y(x))} \csc \left (\frac {y(x)}{2}\right ) \sec \left (\frac {y(x)}{2}\right ) \left (\log \left (\sec ^2\left (\frac {y(x)}{2}\right )\right )-2 \log \left (\tan \left (\frac {y(x)}{2}\right )\right )\right )=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.785 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1/tan(y(x)) - 1/sin(y(x)))*sin(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \int \limits ^{y{\left (x \right )}} \frac {\sin {\left (y \right )} \tan {\left (y \right )}}{\sin {\left (y \right )} - \tan {\left (y \right )}}\, dy = C_{1} + \cos {\left (x \right )} \]