90.4.2 problem 2

Internal problem ID [25097]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:50:06 PM
CAS classification : [_linear]

\begin{align*} \cos \left (t \right ) y^{\prime }+\sin \left (t \right ) y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 11

ode:=cos(t)*diff(y(t),t)+sin(t)*y(t) = 1; 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \sin \left (t \right )+5 \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 12

ode=Cos[t]*D[y[t],{t,1}]+Sin[t]*y[t] == 1; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \sin (t)+5 \cos (t) \end{align*}

✓ Sympy. Time used: 0.425 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)*sin(t) + cos(t)*Derivative(y(t), t) - 1,0) 
ics = {y(0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \sin {\left (t \right )} + 5 \cos {\left (t \right )} \]