84.12.4 problem 6.9

Internal problem ID [22146]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Supplementary problems
Problem number : 6.9
Date solved : Thursday, October 02, 2025 at 08:32:25 PM
CAS classification : [_separable]

\begin{align*} x \,{\mathrm e}^{y x}+y \,{\mathrm e}^{y x} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {-x^{2}+c_1} \\ y &= -\sqrt {-x^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to -\sqrt {-x^2+2 c_1}\\ y(x)&\to \sqrt {-x^2+2 c_1} \end{align*}

✓ Sympy. Time used: 0.246 (sec). Leaf size: 22

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} - x^{2}}\right ] \]