Internal problem ID [11383]
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(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {Q^{\prime }-\frac {Q}{4+Q^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(Q(t),t)=Q(t)/(4+Q(t)^2),Q(t), singsol=all)
\[ Q \left (t \right ) = {\mathrm e}^{-\frac {\operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {t}{2}+\frac {c_{1}}{2}}}{4}\right )}{2}+\frac {t}{4}+\frac {c_{1}}{4}} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 42
DSolve[Q'[t]==Q[t]/(4*Q[t]^2),Q[t],t,IncludeSingularSolutions -> True]
\begin{align*} Q(t)\to -\frac {\sqrt {t+4 c_1}}{\sqrt {2}} Q(t)\to \frac {\sqrt {t+4 c_1}}{\sqrt {2}} \end{align*}