Internal problem ID [10368]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-x \left (4+x\right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(x(t),t)=x(t)*(4+x(t)),x(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {4}{-1+5 \,{\mathrm e}^{-4 t}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 18
DSolve[{x'[t]==x[t]*(4+x[t]),{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {20}{e^{4 t}-5}-4 \\ \end{align*}