Internal problem ID [2209]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page
91
Problem number: Problem 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{2}-2 x +2 y y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve((y(x)^2-2*x)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {x \left (x^{2}+c_{1}\right )}}{x} \\ y \relax (x ) = -\frac {\sqrt {x \left (x^{2}+c_{1}\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.213 (sec). Leaf size: 42
DSolve[(y[x]^2-2*x)+2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ \end{align*}