Internal problem ID [536]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 \arctan \relax (y)}{1+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 22
dsolve(diff(y(t),t) = -2*arctan(y(t))/(1+y(t)^2),y(t), singsol=all)
\[ t +\int _{}^{y \relax (t )}\frac {\textit {\_a}^{2}+1}{2 \arctan \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.903 (sec). Leaf size: 38
DSolve[y'[t] == -2*ArcTan[y[t]]/(1+y[t]^2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {K[1]^2+1}{\text {ArcTan}(K[1])}dK[1]\&\right ][-2 t+c_1] \\ y(t)\to 0 \\ \end{align*}