68.4.58 problem 57 (b)

Internal problem ID [17238]
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 : Thursday, October 02, 2025 at 01:59:31 PM
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*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 12

ode:=diff(y(t),t) = y(t)^2*cos(t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 21

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

\begin{align*} y(t)&\to \frac {1}{1-\int _0^t\cos (K[1])dK[1]} \end{align*}

✓ Sympy. Time used: 0.109 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**2*cos(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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