76.2.9 problem 9

Internal problem ID [17274]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 9
Date solved : Monday, March 31, 2025 at 03:48:21 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 37

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

\[ y(t)\to e^{-t/2} \left (\int _1^t\frac {3}{2} e^{\frac {K[1]}{2}} K[1]dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.141 (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)
 

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