69.11.9 problem 268

Internal problem ID [18147]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 268
Date solved : Thursday, October 02, 2025 at 03:02:08 PM
CAS classification : [_quadrature]

\begin{align*} \left (y^{\prime }-1\right )^{2}&=y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\begin{align*} y &= -1+{\mathrm e}^{x} c_1 \\ y &= 1+{\mathrm e}^{-x} c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to 1+c_1 e^{-x}\\ y(x)&\to -1+c_1 e^x\\ y(x)&\to -1\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 17

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

\[ \left [ y{\left (x \right )} = C_{1} e^{x} - 1, \ y{\left (x \right )} = C_{1} e^{- x} + 1\right ] \]