50.5.1 problem 1(a)

Internal problem ID [7871]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:29:09 PM
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: 0.004 (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: 0.546 (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*}