62.16.4 problem Ex 4

Internal problem ID [12824]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 27. Clairaut equation. Page 56
Problem number : Ex 4
Date solved : Monday, March 31, 2025 at 07:11:56 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 1.950 (sec). Leaf size: 24

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

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

✗ Mathematica

ode=Exp[2*y[x]]*(D[y[x],x])^3+(Exp[2*x]+Exp[3*x])*D[y[x],x]-Exp[3*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))*Derivative(y(x), x) - exp(3*x) + exp(2*y(x))*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out