10.1.9 problem 9

Internal problem ID [1106]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 9
Date solved : Saturday, March 29, 2025 at 10:39:10 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y+2 y^{\prime }&=3 t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=y(t)+2*diff(y(t),t) = 3*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 3 t -6+{\mathrm e}^{-\frac {t}{2}} c_1 \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 20

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

\[ y(t)\to 3 t+c_1 e^{-t/2}-6 \]

✓ Sympy. Time used: 0.135 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{1} e^{- \frac {t}{2}} + 3 t - 6 \]