Internal problem ID [1914]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2}+y^{2}-2 y y^{\prime } x=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 23
dsolve([(x^2+y(x)^2)=2*x*y(x)*diff(y(x),x),y(-1) = 0],y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x \left (x +1\right )} \\ y \relax (x ) = -\sqrt {x \left (x +1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.22 (sec). Leaf size: 36
DSolve[{(x^2+y[x]^2)==2*x*y[x]*y'[x],y[-1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+1} \\ y(x)\to \sqrt {x} \sqrt {x+1} \\ \end{align*}