10.1.28 problem 28

Internal problem ID [1125]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 28
Date solved : Saturday, March 29, 2025 at 10:40:32 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} \frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \end{align*}

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

ode:=2/3*y(t)+diff(y(t),t) = 1-1/2*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {3 t}{4}+\frac {21}{8}+{\mathrm e}^{-\frac {2 t}{3}} c_1 \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 24

ode=2/3*y[t]+D[y[t],t] == 1-1/2*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {3 t}{4}+c_1 e^{-2 t/3}+\frac {21}{8} \]

✓ Sympy. Time used: 0.130 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t/2 + 2*y(t)/3 + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \frac {2 t}{3}} - \frac {3 t}{4} + \frac {21}{8} \]