63.4.4 problem 1(d)

Internal problem ID [13047]
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 : Tuesday, January 28, 2025 at 04:50:08 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

dsolve(diff(u(t),t)=1/(5-2*u(t)),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*}

✓ Solution by Mathematica

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

DSolve[D[u[t],t]==1/(5-2*u[t]),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*}