Internal problem ID [10353]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {u^{\prime }-\frac {1}{5-2 u}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(u(t),t)=1/(5-2*u(t)),u(t), singsol=all)
\begin{align*} u \left (t \right ) = \frac {5}{2}-\frac {\sqrt {25-4 t -4 c_{1}}}{2} \\ u \left (t \right ) = \frac {5}{2}+\frac {\sqrt {25-4 t -4 c_{1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 49
DSolve[u'[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*}