75.11.4 problem 263

Internal problem ID [16776]
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 : 263
Date solved : Thursday, March 13, 2025 at 08:45:14 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 28

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

\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to c_1 e^x \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 14

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

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