78.1.28 problem 2 (n)

Internal problem ID [18004]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (n)
Date solved : Thursday, March 13, 2025 at 11:18:57 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \sin \left (x \right )&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(y(x),x)*sin(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\ln \left (\csc \left (x \right )+\cot \left (x \right )\right )+c_{1} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 13

ode=D[y[x],x]*Sin[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\text {arctanh}(\cos (x))+c_1 \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (\cos {\left (x \right )} - 1 \right )}}{2} - \frac {\log {\left (\cos {\left (x \right )} + 1 \right )}}{2} \]