78.3.1 problem 1 (a)

Internal problem ID [18104]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 11:26:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve((x^2-2*y(x)^2)+x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {c_1 \,x^{2}+1}\, x \\ y &= -\sqrt {c_1 \,x^{2}+1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.566 (sec). Leaf size: 39

DSolve[(x^2-2*y[x]^2)+x*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x^2+c_1 x^4} \\ y(x)\to \sqrt {x^2+c_1 x^4} \\ \end{align*}