89.3.24 problem 25

Internal problem ID [24322]
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 34
Problem number : 25
Date solved : Thursday, October 02, 2025 at 10:18:00 PM
CAS classification : [_exact]

\begin{align*} y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.095 (sec). Leaf size: 22

ode:=y(x)*exp(x*y(x))-2*y(x)^3+(x*exp(x*y(x))-6*x*y(x)^2-2*y(x))*diff(y(x),x) = 0; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (2 x \,\textit {\_Z}^{3}+\textit {\_Z}^{2}-{\mathrm e}^{x \textit {\_Z}}-3\right ) \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 25

ode=( y[x]*Exp[ x*y[x]] -2*y[x]^3 )+ ( x*Exp[x*y[x]] - 6*x*y[x]^2 -2*y[x]  )*D[y[x],x]==0; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 x y(x)^3+y(x)^2-e^{x y(x)}=3,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-6*x*y(x)**2 + x*exp(x*y(x)) - 2*y(x))*Derivative(y(x), x) - 2*y(x)**3 + y(x)*exp(x*y(x)),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out