Internal problem ID [4426]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 t \left (\cos ^{2}\relax (y)\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 10
dsolve([diff(y(t),t)=2*t*cos(y(t))^2,y(0) = 1/4*Pi],y(t), singsol=all)
\[ y \relax (t ) = \arctan \left (t^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 11
DSolve[{y'[t]==2*t*Cos[y[t]]^2,{y[0]==Pi/4}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {ArcTan}\left (t^2+1\right ) \\ \end{align*}