10.4.5 problem 6

Internal problem ID [1186]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:43:23 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-\frac {2 \arctan \left (y\right )}{1+y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(t),t) = -2*arctan(y(t))/(1+y(t)^2),y(t), singsol=all)
 

\[ t +\frac {\left (\int _{}^{y}\frac {\textit {\_a}^{2}+1}{\arctan \left (\textit {\_a} \right )}d \textit {\_a} \right )}{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.959 (sec). Leaf size: 38

DSolve[D[y[t],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*}