63.4.6 problem 1(f)

Internal problem ID [13049]
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)
Date solved : Tuesday, January 28, 2025 at 04:50:10 AM
CAS classification : [_quadrature]

\begin{align*} Q^{\prime }&=\frac {Q}{4+Q^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 38

dsolve(diff(Q(t),t)=Q(t)/(4+Q(t)^2),Q(t), singsol=all)
 

\[ Q = \frac {2 \,{\mathrm e}^{\frac {t}{4}+\frac {c_{1}}{4}}}{\sqrt {\frac {{\mathrm e}^{\frac {t}{2}+\frac {c_{1}}{2}}}{\operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {t}{2}+\frac {c_{1}}{2}}}{4}\right )}}} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 42

DSolve[D[ Q[t],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*}