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 : Monday, January 27, 2025 at 03:04:12 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

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

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