Internal problem ID [2718]
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]
\[ \boxed {y^{2}+2 x y y^{\prime }=2 x} \]
✓ 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 \left (x \right ) &= \frac {\sqrt {x \left (x^{2}+c_{1} \right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (x^{2}+c_{1} \right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.207 (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*}