Internal problem ID [11660]
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 (iii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-\left (x+1\right ) \left (-x+2\right ) \sin \left (x\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(x(t),t)=(1+x(t))*(2-x(t))*sin(x(t)),x(t), singsol=all)
\[ t +\int _{}^{x \left (t \right )}\frac {1}{\left (\textit {\_a} +1\right ) \left (\textit {\_a} -2\right ) \sin \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 15.593 (sec). Leaf size: 52
DSolve[x'[t]==(1+x[t])*(2-x[t])*Sin[x[t]],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\csc (K[1])}{(K[1]-2) (K[1]+1)}dK[1]\&\right ][-t+c_1] x(t)\to -1 x(t)\to 0 x(t)\to 2 \end{align*}