89.4.12 problem 13

Internal problem ID [24334]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:18:32 PM
CAS classification : [NONE]

\begin{align*} y \left (x^{3} {\mathrm e}^{y x}-y\right )+x \left (y+x^{3} {\mathrm e}^{y x}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 19

ode:=y(x)*(x^3*exp(x*y(x))-y(x))+x*(y(x)+x^3*exp(x*y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ {\mathrm e}^{x y}+\frac {y^{2}}{2 x^{2}}+c_1 = 0 \]

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 30

ode=y[x]*( x^3*Exp[x*y[x]]-y[x] )+x*( y[x]+ x^3*Exp[x*y[x]] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [y(x) \left (\frac {y(x)}{2 x^2}+\frac {e^{x y(x)}}{y(x)}\right )=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**3*exp(x*y(x)) + y(x))*Derivative(y(x), x) + (x**3*exp(x*y(x)) - y(x))*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out