27.1.2 problem 2

Internal problem ID [4296]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 2
Date solved : Monday, January 27, 2025 at 08:50:09 AM
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*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.445 (sec). Leaf size: 40

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

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