10.1.30 problem 30

Internal problem ID [1127]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 30
Date solved : Tuesday, March 04, 2025 at 12:10:33 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} -y+y^{\prime }&=1+3 \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=-y(t)+diff(y(t),t) = 1+3*sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -1-\frac {3 \cos \left (t \right )}{2}-\frac {3 \sin \left (t \right )}{2}+{\mathrm e}^{t} c_1 \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 25

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

\[ y(t)\to -\frac {3 \sin (t)}{2}-\frac {3 \cos (t)}{2}+c_1 e^t-1 \]

✓ Sympy. Time used: 0.137 (sec). Leaf size: 22

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

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