74.4.58 problem 57 (b)

Internal problem ID [15951]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 57 (b)
Date solved : Tuesday, January 28, 2025 at 08:24:27 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 12

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

\[ y = -\frac {1}{-1+\sin \left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 21

DSolve[{D[y[t],t]==y[t]^2*Cos[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{1-\int _0^t\cos (K[1])dK[1]} \]