44.4.16 problem 16

Internal problem ID [9151]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 06:08:28 PM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 18

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

\[ \csc \left (y\right ) \cot \left (x \right )+x \,{\mathrm e}^{y^{2}}+c_1 = 0 \]

✓ Mathematica. Time used: 135.604 (sec). Leaf size: 2204

ode=(Exp[y[x]^2]-Csc[y[x]]*Csc[x]^2)+(2*x*y[x]*Exp[y[x]^2]-Csc[y[x]]*Cot[y[x]]*Cot[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((2*x*y(x)*exp(y(x)**2) - 1/(sin(y(x))*tan(x)*tan(y(x))))*Derivative(y(x), x) + exp(y(x)**2) - 1/(sin(x)**2*sin(y(x))),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out