7.5.59 problem 59

Internal problem ID [163]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 59
Date solved : Friday, February 07, 2025 at 07:59:19 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+3} \end{align*}

✓ Solution by Maple

Time used: 0.255 (sec). Leaf size: 32

dsolve(diff(y(x),x)= (x-y(x)-1)/(x+y(x)+3),y(x), singsol=all)
 

\[ y = \frac {-\sqrt {2 \left (x +1\right )^{2} c_1^{2}+1}+\left (-x -3\right ) c_1}{c_1} \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 53

DSolve[D[y[x],x]==(x-y[x]-1)/(x+y[x]+3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2 x^2+4 x+9+c_1}-x-3 \\ y(x)\to \sqrt {2 x^2+4 x+9+c_1}-x-3 \\ \end{align*}