48.1.14 problem Example 3.15

Internal problem ID [7515]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.15
Date solved : Sunday, March 30, 2025 at 12:13:21 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 0.205 (sec). Leaf size: 17

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

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