29.35.7 problem 1039

Internal problem ID [5605]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1039
Date solved : Sunday, March 30, 2025 at 09:08:02 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.528 (sec). Leaf size: 28

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

\[ y = -\frac {\ln \left (-\frac {{\mathrm e}^{2 x}}{\left (c_1 +1\right ) \left (-c_1 +{\mathrm e}^{x}\right )^{2}}\right )}{2}+x \]

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out