16.1.12 problem 3(f)

Internal problem ID [3414]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(f)
Date solved : Tuesday, March 04, 2025 at 04:38:08 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.039 (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: 0.136 (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)
 

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