Internal problem ID [5139]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page
218
Problem number: Problem 3.32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x^{2}-y^{2}+2 x y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((x^2-y(x)^2)+2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {c_{1} x -x^{2}} \\ y \left (x \right ) = -\sqrt {c_{1} x -x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.334 (sec). Leaf size: 35
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 (-x+c_1)} \\ y(x)\to \sqrt {x (-x+c_1)} \\ \end{align*}