74.4.58 problem 57 (b)

Internal problem ID [15872]
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, March 13, 2025 at 06:55:26 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*}

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

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

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

✓ Mathematica. Time used: 0.114 (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]
 

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

✓ Sympy. Time used: 0.199 (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)
 

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