Internal problem ID [2626]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.1
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +y+\left (x -y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.035 (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 \relax (x ) = \left (1+\sqrt {2}\right ) x \\ y \relax (x ) = -\left (\sqrt {2}-1\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 40
DSolve[{(x+y[x])+(x-y[x])*y'[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*}