4.2 problem Problem 3.2

Internal problem ID [5123]

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 3.6 Summary and Problems. Page 218
Problem number: Problem 3.2.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

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

Solution by Maple

Time used: 0.177 (sec). Leaf size: 68

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

\begin{align*} y \relax (x ) = -a \\ y \relax (x ) = a \\ y \relax (x ) = -\tan \left (c_{1}-x \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (c_{1}-x \right )+1}} \\ y \relax (x ) = \tan \left (c_{1}-x \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (c_{1}-x \right )+1}} \\ \end{align*}

Solution by Mathematica

Time used: 2.669 (sec). Leaf size: 111

DSolve[(y'[x])^2==a^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to \frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to -\frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to \frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}