30.3.21 problem 22

Internal problem ID [7477]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 22
Date solved : Tuesday, September 30, 2025 at 04:38:06 PM
CAS classification : [_exact]

\begin{align*} y \,{\mathrm e}^{x y}-\frac {1}{y}+\left (x \,{\mathrm e}^{x y}+\frac {x}{y^{2}}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.110 (sec). Leaf size: 21

ode:=y(x)*exp(x*y(x))-1/y(x)+(x*exp(x*y(x))+x/y(x)^2)*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 21

ode=( y[x]*Exp[x*y[x]] -1/y[x] )+( x*Exp[x*y[x]]+x/y[x]^2   )*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [e^{x y(x)}-\frac {x}{y(x)}=e-1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x*exp(x*y(x)) + x/y(x)**2)*Derivative(y(x), x) + y(x)*exp(x*y(x)) - 1/y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out