Internal problem ID [5465]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-y^{2} x +1}{2 y x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (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 \relax (x ) = \frac {\sqrt {x \left (\ln \relax (x )+c_{1}\right )}}{x} \\ y \relax (x ) = -\frac {\sqrt {x \left (\ln \relax (x )+c_{1}\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.169 (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*}