Internal problem ID [3929]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.12, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {-2 y y^{\prime } x +y^{2}+x^{2}=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 {\left (x +1\right ) x} \\ y \relax (x ) = -\sqrt {\left (x +1\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.178 (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*}