44.4.7 problem 7

Internal problem ID [9142]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 06:06:53 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 16

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

\[ c_1 +\sin \left (x \right ) \cos \left (y\right )+x \,{\mathrm e}^{y} = 0 \]

✓ Mathematica. Time used: 0.425 (sec). Leaf size: 97

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

\[ \text {Solve}\left [\int _1^x\left (\cos (K[1]-y(x))+2 e^{y(x)}+\cos (K[1]+y(x))\right )dK[1]+\int _1^{y(x)}\left (2 e^{K[2]} x-\cos (x-K[2])+\cos (x+K[2])-\int _1^x\left (\sin (K[1]-K[2])+2 e^{K[2]}-\sin (K[1]+K[2])\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out