81.4.19 problem 5-20

Internal problem ID [21533]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-20
Date solved : Thursday, October 02, 2025 at 07:46:58 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \end{align*}

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

ode:=exp(x)-sin(y(x))+cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\arcsin \left (\left (x +c_1 \right ) {\mathrm e}^{x}\right ) \]

✓ Mathematica. Time used: 10.834 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to -\arcsin \left (e^x (x+c_1)\right ) \end{align*}

✓ Sympy. Time used: 1.285 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\left (C_{1} + x\right ) e^{x} \right )} + \pi , \ y{\left (x \right )} = - \operatorname {asin}{\left (\left (C_{1} + x\right ) e^{x} \right )}\right ] \]