49.22.6 problem 1(f)

Internal problem ID [7752]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(f)
Date solved : Monday, January 27, 2025 at 03:12:03 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (x -y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.158 (sec). Leaf size: 49

dsolve((x+y(x))+(x-y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.448 (sec). Leaf size: 86

DSolve[(x+y[x])+(x-y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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