74.1.33 problem 40

Internal problem ID [15813]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 08:08:03 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {-2 x -10}{\left (x +2\right ) \left (x -4\right )} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(x),x)=(-2*(x+5))/((x+2)*(x-4)),y(x), singsol=all)
 

\[ y = -3 \ln \left (x -4\right )+\ln \left (x +2\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 33

DSolve[D[y[x],x]==(-2*(x+5))/((x+2)*(x-4)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x-\frac {2 (K[1]+5)}{K[1]^2-2 K[1]-8}dK[1]+c_1 \]