Internal problem ID [6203]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {-2 y^{2}+x y y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \sqrt {c_{1} x^{2}+1}\, x y \left (x \right ) = -\sqrt {c_{1} x^{2}+1}\, x \end{align*}
✓ Solution by Mathematica
Time used: 0.451 (sec). Leaf size: 39
DSolve[(x^2-2*y[x]^2)+(x*y[x])*y'[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*}