Internal problem ID [6218]
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: 5(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {-x y^{2}+1}{2 y x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x)=(1-x*y(x)^2)/(2*x^2*y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {x \left (\ln \left (x \right )+c_{1} \right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (\ln \left (x \right )+c_{1} \right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 40
DSolve[y'[x]==(1-x*y[x]^2)/(2*x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\log (x)+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {\log (x)+c_1}}{\sqrt {x}} \\ \end{align*}