82.18.21 problem Ex. 23

Internal problem ID [18772]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 23
Date solved : Monday, March 31, 2025 at 06:10:06 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`], _dAlembert]

\begin{align*} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y}&=0 \end{align*}

✓ Maple. Time used: 0.267 (sec). Leaf size: 44

ode:=exp(3*x)*(diff(y(x),x)-1)+diff(y(x),x)^3*exp(2*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \ln \left (2\right )-\frac {3 \ln \left (3\right )}{2}+\frac {i \pi }{2}+\frac {3 x}{2} \\ y &= \frac {\ln \left (-{\mathrm e}^{-x} c_1 \left ({\mathrm e}^{-x} c_1 -1\right )^{2}\right )}{2}+\frac {3 x}{2} \\ \end{align*}

✗ Mathematica

ode=Exp[3*x]*(D[y[x],x]-1)+D[y[x],x]^3*Exp[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((Derivative(y(x), x) - 1)*exp(3*x) + exp(2*y(x))*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out