63.4.19 problem 9

Internal problem ID [13062]
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
Date solved : Tuesday, January 28, 2025 at 04:50:51 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=x \left (4+x\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.029 (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: 0.009 (sec). Leaf size: 21

DSolve[{D[x[t],t]==x[t]*(4+x[t]),{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {4 e^{4 t}}{e^{4 t}-5} \]