73.1.18 problem 2.3 (h)

Internal problem ID [14996]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (h)
Date solved : Tuesday, January 28, 2025 at 07:27:12 AM
CAS classification : [_quadrature]

\begin{align*} 1&=\left (x^{2}-9\right ) y^{\prime } \end{align*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(1=(x^2-9)*diff(y(x),x),y(x), singsol=all)
 
\[ y = \frac {\ln \left (x -3\right )}{6}-\frac {\ln \left (x +3\right )}{6}+c_{1} \]

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 23

DSolve[1==(x^2-9)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \int _1^x\frac {1}{K[1]^2-9}dK[1]+c_1 \]