74.11.18 problem 30

Internal problem ID [16189]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 30
Date solved : Thursday, March 13, 2025 at 07:55:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=-32 t^{2} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 37

ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)-4*y(t) = -32*t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (8 t^{2}+12 t +13\right ) {\mathrm e}^{-4 t} {\mathrm e}^{4 t}+\left (c_{1} {\mathrm e}^{5 t}+c_{2} \right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

ode=D[y[t],{t,2}]+3*D[y[t],t]-4*y[t]==-32*t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 8 t^2+12 t+c_1 e^{-4 t}+c_2 e^t+13 \]

✓ Sympy. Time used: 0.185 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(32*t**2 - 4*y(t) + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{t} + 8 t^{2} + 12 t + 13 \]