78.4.15 problem 16

Internal problem ID [18067]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 16
Date solved : Monday, March 31, 2025 at 05:02:47 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: 0.036 (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: 147.872 (sec). Leaf size: 23

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]
 

\[ \text {Solve}\left [-2 x e^{y(x)^2}-2 \cot (x) \csc (y(x))=c_1,y(x)\right ] \]

✗ 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