8.5.37 problem 37

Internal problem ID [765]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 37
Date solved : Saturday, March 29, 2025 at 10:21:08 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.179 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}}-\ln \left (-\textit {\_Z} x -c_1 -\sin \left (x \right )\right )\right )} \]

✓ Mathematica. Time used: 0.348 (sec). Leaf size: 18

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

\[ \text {Solve}\left [e^{y(x)}+x \log (y(x))+\sin (x)=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out