Internal problem ID [4414]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x v^{\prime }-\frac {1-4 v^{2}}{3 v}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 43
dsolve(x*diff(v(x),x)=(1-4*v(x)^2)/(3*v(x)),v(x), singsol=all)
\begin{align*} v \relax (x ) = -\frac {\sqrt {x^{\frac {8}{3}} \left (x^{\frac {8}{3}}+4 c_{1}\right )}}{2 x^{\frac {8}{3}}} \\ v \relax (x ) = \frac {\sqrt {x^{\frac {8}{3}} \left (x^{\frac {8}{3}}+4 c_{1}\right )}}{2 x^{\frac {8}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 67
DSolve[x*v'[x]==(1-4*v[x]^2)/(3*v[x]),v[x],x,IncludeSingularSolutions -> True]
\begin{align*} v(x)\to -\frac {1}{2} \sqrt {1+\frac {e^{8 c_1}}{x^{8/3}}} \\ v(x)\to \frac {1}{2} \sqrt {1+\frac {e^{8 c_1}}{x^{8/3}}} \\ v(x)\to -\frac {1}{2} \\ v(x)\to \frac {1}{2} \\ \end{align*}