Internal problem ID [4922]
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]
\[ \boxed {x v^{\prime }-\frac {1-4 v^{2}}{3 v}=0} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) = -\frac {\sqrt {x^{\frac {8}{3}} \left (x^{\frac {8}{3}}+4 c_{1} \right )}}{2 x^{\frac {8}{3}}} v \left (x \right ) = \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: 1.93 (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*}