Internal problem ID [11662]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 7, Scalar autonomous ODEs. Exercises page 56
Problem number: 7.1 (v).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-x^{2}+x^{4}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 47
dsolve(diff(x(t),t)=x(t)^2-x(t)^4,x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right ) {\mathrm e}^{\textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2 t \,{\mathrm e}^{\textit {\_Z}}-\ln \left ({\mathrm e}^{\textit {\_Z}}-2\right )-2 c_{1} +\textit {\_Z} -2 t +2\right )}-1 \]
✓ Solution by Mathematica
Time used: 0.414 (sec). Leaf size: 53
DSolve[x'[t]==x[t]^2-x[t]^4,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\frac {1}{2} \log (1-\text {$\#$1})-\frac {1}{2} \log (\text {$\#$1}+1)\&\right ][-t+c_1] x(t)\to -1 x(t)\to 0 x(t)\to 1 \end{align*}