23.2.349 problem 399

Internal problem ID [5704]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 399
Date solved : Tuesday, September 30, 2025 at 02:00:48 PM
CAS classification : [_quadrature]

\begin{align*} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 31

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

\[ x -\int _{}^{y}\frac {1}{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z} -\textit {\_a}}+\textit {\_Z}^{2}-1\right )}d \textit {\_a} -c_1 = 0 \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 49

ode=Exp[D[y[x],x]-y[x]]-(D[y[x],x])^2+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\left \{x=\int \frac {1-\frac {2 K[1]}{K[1]^2-1}}{K[1]} \, dK[1]+c_1,y(x)=K[1]-\log \left (K[1]^2-1\right )\right \},\{y(x),K[1]\}\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(exp(-y(x) + Derivative(y(x), x)) - Derivative(y(x), x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, exp(_X0)] 
No algorithms are implemented to solve equation -_X0**2*exp(y(x)) + exp(_X0) + exp(y(x))