36.1.11 problem 11

Internal problem ID [6266]
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
Date solved : Monday, January 27, 2025 at 01:50:34 PM
CAS classification : [_separable]

\begin{align*} x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \end{align*}

✓ 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 \left (x \right ) &= -\frac {\sqrt {x^{{8}/{3}} \left (x^{{8}/{3}}+4 c_{1} \right )}}{2 x^{{8}/{3}}} \\ v \left (x \right ) &= \frac {\sqrt {x^{{8}/{3}} \left (x^{{8}/{3}}+4 c_{1} \right )}}{2 x^{{8}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.919 (sec). Leaf size: 67

DSolve[x*D[v[x],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*}