36.1.23 problem 23

Internal problem ID [6278]
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
Date solved : Monday, January 27, 2025 at 01:53:01 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 t \cos \left (y\right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\pi }{4} \end{align*}

✓ Solution by Maple

Time used: 0.093 (sec). Leaf size: 10

dsolve([diff(y(t),t)=2*t*cos(y(t))^2,y(0) = 1/4*Pi],y(t), singsol=all)
 

\[ y = \arctan \left (t^{2}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 11

DSolve[{D[y[t],t]==2*t*Cos[y[t]]^2,{y[0]==Pi/4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \arctan \left (t^2+1\right ) \]