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 : Monday, January 27, 2025 at 07:36:05 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

dsolve((diff(y(x),x))^2-y(x)^2=0,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*}

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 28

DSolve[(D[y[x],x])^2-y[x]^2==0,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*}