20.5.6 problem Problem 6

Internal problem ID [3689]
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
Date solved : Monday, January 27, 2025 at 07:55:24 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} y^{2}-2 x +2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.205 (sec). Leaf size: 42

DSolve[(y[x]^2-2*x)+2*x*y[x]*D[y[x],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*}