48.4.2 problem Problem 3.2

Internal problem ID [7544]
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
Date solved : Monday, January 27, 2025 at 03:05:07 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 60

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

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

✓ Solution by Mathematica

Time used: 3.364 (sec). Leaf size: 111

DSolve[(D[y[x],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*}