Internal problem ID [12655]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {w^{\prime }-\left (w^{2}-2\right ) \arctan \left (w\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(w(t),t)=(w(t)^2-2)*arctan( w(t) ),w(t), singsol=all)
\[ t -\left (\int _{}^{w \left (t \right )}\frac {1}{\left (\textit {\_a}^{2}-2\right ) \arctan \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.909 (sec). Leaf size: 62
DSolve[w'[t]==(w[t]^2-2)*Arctan[ w[t]],w[t],t,IncludeSingularSolutions -> True]
\begin{align*} w(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\text {Arctan}(K[1]) \left (K[1]^2-2\right )}dK[1]\&\right ][t+c_1] w(t)\to -\sqrt {2} w(t)\to \sqrt {2} w(t)\to \text {Arctan}^{(-1)}(0) \end{align*}