57.3.8 problem 8

Internal problem ID [9065]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 8
Date solved : Wednesday, March 05, 2025 at 07:18:54 AM
CAS classification : [_linear]

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

Using Laplace method With initial conditions

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

✗ Maple

ode:=t*diff(y(t),t)+y(t) = sin(t); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 16

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

\[ y(t)\to \frac {\cos (1)-\cos (t)}{t} \]

✓ Sympy. Time used: 0.252 (sec). Leaf size: 10

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

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