4.19 problem Problem 3.32

Internal problem ID [5140]

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]

Solve \begin {gather*} \boxed {x^{2}-y^{2}+2 x y y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.016 (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 \relax (x ) = \sqrt {-x^{2}+c_{1} x} \\ y \relax (x ) = -\sqrt {-x^{2}+c_{1} x} \\ \end{align*}

Solution by Mathematica

Time used: 0.453 (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*}