63.4.4 problem 1(d)

Internal problem ID [12968]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 1(d)
Date solved : Wednesday, March 05, 2025 at 08:55:13 PM
CAS classification : [_quadrature]

\begin{align*} u^{\prime }&=\frac {1}{5-2 u} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

ode:=diff(u(t),t) = 1/(5-2*u(t)); 
dsolve(ode,u(t), singsol=all);
 

\begin{align*} u &= \frac {5}{2}-\frac {\sqrt {25-4 t -4 c_{1}}}{2} \\ u &= \frac {5}{2}+\frac {\sqrt {25-4 t -4 c_{1}}}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 49

ode=D[u[t],t]==1/(5-2*u[t]); 
ic={}; 
DSolve[{ode,ic},u[t],t,IncludeSingularSolutions->True]
 

\begin{align*} u(t)\to \frac {1}{2} \left (5-\sqrt {-4 t+25+4 c_1}\right ) \\ u(t)\to \frac {1}{2} \left (5+\sqrt {-4 t+25+4 c_1}\right ) \\ \end{align*}

✓ Sympy. Time used: 0.392 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
u = Function("u") 
ode = Eq(Derivative(u(t), t) - 1/(5 - 2*u(t)),0) 
ics = {} 
dsolve(ode,func=u(t),ics=ics)
 

\[ \left [ u{\left (t \right )} = \frac {5}{2} - \frac {\sqrt {C_{1} - 4 t}}{2}, \ u{\left (t \right )} = \frac {\sqrt {C_{1} - 4 t}}{2} + \frac {5}{2}\right ] \]