7.1.1 problem Example 3

Internal problem ID [2294]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 3
Date solved : Tuesday, September 30, 2025 at 05:26:03 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\sin \left (t \right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {3}{2}} \\ \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 11

ode:=diff(y(t),t)+sin(t)*y(t) = 0; 
ic:=[y(0) = 3/2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {3 \,{\mathrm e}^{-1+\cos \left (t \right )}}{2} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

ode=D[y[t],t]+Sin[t]*y[t]==0; 
ic=y[0]==3/2; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {3}{2} e^{\cos (t)-1} \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)*sin(t) + Derivative(y(t), t),0) 
ics = {y(0): 3/2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {3 e^{\cos {\left (t \right )}}}{2 e} \]