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]
\[ \boxed {y^{\prime }+\frac {2 \arctan \left (y\right )}{1+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t) = -2*arctan(y(t))/(1+y(t)^2),y(t), singsol=all)
\[ t +\frac {\left (\int _{}^{y \left (t \right )}\frac {\textit {\_a}^{2}+1}{\arctan \left (\textit {\_a} \right )}d \textit {\_a} \right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.013 (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}{\arctan (K[1])}dK[1]\&\right ][-2 t+c_1] \\ y(t)\to 0 \\ \end{align*}