14.2.12 problem 12

Internal problem ID [2500]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 12
Date solved : Sunday, March 30, 2025 at 12:03:49 AM
CAS classification : [_separable]

\begin{align*} 3 t y^{\prime }&=y \cos \left (t \right ) \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 5

ode:=3*t*diff(y(t),t) = y(t)*cos(t); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=3*t*D[y[t],t]==y[t]*Cos[t]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 0 \]

✓ Sympy. Time used: 0.690 (sec). Leaf size: 3

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t*Derivative(y(t), t) - y(t)*cos(t),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 0 \]