85.33.55 problem 55

Internal problem ID [22678]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 55
Date solved : Thursday, October 02, 2025 at 09:06:16 PM
CAS classification : [_separable]

\begin{align*} u v-2 v+\left (-u^{2}+u \right ) v^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=u*v(u)-2*v(u)+(-u^2+u)*diff(v(u),u) = 0; 
dsolve(ode,v(u), singsol=all);
 

\[ v = \frac {c_1 \,u^{2}}{u -1} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 23

ode=(u*v[u]-2*v[u])+(u-u^2)*D[v[u],u]==0; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

\begin{align*} v(u)&\to \frac {c_1 u^2}{1-u}\\ v(u)&\to 0 \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 10

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

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