80.6.7 problem 9 (a)

Internal problem ID [18500]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 9 (a)
Date solved : Monday, March 31, 2025 at 05:38:23 PM
CAS classification : [_separable]

\begin{align*} v^{\prime }+\frac {2 v}{u}&=3 v \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(v(u),u)+2*v(u)/u = 3*v(u); 
dsolve(ode,v(u), singsol=all);
 

\[ v = \frac {c_1 \,{\mathrm e}^{3 u}}{u^{2}} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 21

ode=D[v[u],u]+2*v[u]/u==3*v[u]; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\begin{align*} v(u)\to \frac {c_1 e^{3 u}}{u^2} \\ v(u)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.269 (sec). Leaf size: 12

from sympy import * 
u = symbols("u") 
v = Function("v") 
ode = Eq(-3*v(u) + Derivative(v(u), u) + 2*v(u)/u,0) 
ics = {} 
dsolve(ode,func=v(u),ics=ics)
 

\[ v{\left (u \right )} = \frac {C_{1} e^{3 u}}{u^{2}} \]