Internal problem ID [10145]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating
factors by inspection. Page 23
Problem number: Ex 4.
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 x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((x^2+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+x c_{1}} \\ y \relax (x ) = -\sqrt {x^{2}+x c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 38
DSolve[(x^2+y[x]^2)-2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ \end{align*}