1.14 problem Example 3.15

Internal problem ID [5094]

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.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-y^{2} a^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 31

DSolve[(y'[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*}