72.8.16 problem 29

Internal problem ID [14701]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 29
Date solved : Thursday, March 13, 2025 at 04:15:30 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {t^{2}}{3}-\frac {2 t}{9}+\frac {2}{27}+{\mathrm e}^{-2 t}+{\mathrm e}^{-3 t} c_{1} \]

✓ Mathematica. Time used: 0.205 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.176 (sec). Leaf size: 29

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

\[ y{\left (t \right )} = C_{1} e^{- 3 t} + \frac {t^{2}}{3} - \frac {2 t}{9} + \frac {2}{27} + e^{- 2 t} \]