Internal problem ID [11994]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }+x \left (k^{2}+x^{2}\right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = x_{0}] \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t)=-x(t)*(k^2+x(t)^2),x(0) = x__0],x(t), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 1.848 (sec). Leaf size: 62
DSolve[{x'[t]==-x[t]*(k^2+x[t]^2),{x[0]==x0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {k}{\sqrt {e^{2 k^2 t} \left (\frac {k^2}{\text {x0}^2}+1\right )-1}} \\ x(t)\to \frac {k}{\sqrt {e^{2 k^2 t} \left (\frac {k^2}{\text {x0}^2}+1\right )-1}} \\ \end{align*}