7.3.12 problem 12

Internal problem ID [2329]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 05:27:10 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.425 (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)
 

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