81.7.5 problem 8-4

Internal problem ID [21579]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 8. Riccati Equation. Page 124.
Problem number : 8-4
Date solved : Thursday, October 02, 2025 at 07:55:45 PM
CAS classification : [_Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

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

\[ y = -\tan \left (-{\mathrm e}^{x}+c_1 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to e^{-x} \tan \left (e^x+c_1\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -y(x)**2*exp(2*x) + y(x) + Derivative(y(x), x) - 1 cannot be solved by the lie group method