74.11.6 problem 18

Internal problem ID [16185]
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 : 18
Date solved : Monday, March 31, 2025 at 02:46:14 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = -\frac {{\mathrm e}^{-2 t} c_1}{2}-t^{2}+\frac {5 t}{2}+c_2 \]

✓ Mathematica. Time used: 4.794 (sec). Leaf size: 46

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

\[ y(t)\to \int _1^te^{-2 K[2]} \left (c_1+\int _1^{K[2]}e^{2 K[1]} (3-4 K[1])dK[1]\right )dK[2]+c_2 \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = C_{1} + C_{2} e^{- 2 t} - t^{2} + \frac {5 t}{2} \]