29.26.22 problem 758

Internal problem ID [5343]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 758
Date solved : Sunday, March 30, 2025 at 08:00:46 AM
CAS classification : [_quadrature]

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

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

ode:=diff(y(x),x)^2 = a^2*y(x)^2; 
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: 0.048 (sec). Leaf size: 31

ode=(D[y[x],x])^2==a^2*y[x]^2; 
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: 0.171 (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)
 

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