28.1.54 problem 55

Internal problem ID [4360]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 55
Date solved : Sunday, March 30, 2025 at 03:10:21 AM
CAS classification : [_quadrature]

\begin{align*} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 1623

ode:=(sin(y(x))^2+x*cot(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.26 (sec). Leaf size: 1647

ode=(Sin[y[x]]^2+x*Cot[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x/tan(y(x)) + sin(y(x))**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : x + sin(y(x))**2*tan(y(x)) is not a solvable differential equation in y(x)