32.4.3 problem Recognizable Exact Differential equations. Integrating factors. Example 10.661, page 90

Internal problem ID [5814]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number : Recognizable Exact Differential equations. Integrating factors. Example 10.661, page 90
Date solved : Sunday, March 30, 2025 at 10:18:36 AM
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: 0.005 (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: 11.852 (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]
 

\[ y(x)\to -\arcsin \left (e^x (x+c_1)\right ) \]

✓ Sympy. Time used: 2.268 (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)
 

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