19.1.3 problem 3

Internal problem ID [4215]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 07:07:30 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 13

ode:=diff(y(x),x) = exp(y(x))*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\cos \left (x \right )-c_1 \right ) \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 15

ode=D[y[x],x]==Exp[y[x]]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\log (\cos (x)-c_1) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \log {\left (- \frac {1}{C_{1} - \cos {\left (x \right )}} \right )} \]