Internal problem ID [2078]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 49.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-2 y^{\prime } y x=-x^{2}} \] With initial conditions \begin {align*} [y \left (2\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 27
dsolve([(x^2+y(x)^2)=2*x*y(x)*diff(y(x),x),y(2) = 0],y(x), singsol=all)
\begin{align*} y = \sqrt {\left (x -2\right ) x} y = -\sqrt {\left (x -2\right ) x} \end{align*}
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 36
DSolve[{(x^2+y[x]^2)==2*x*y[x]*y'[x],{y[2]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x-2} \sqrt {x} y(x)\to \sqrt {x-2} \sqrt {x} \end{align*}