74.18.19 problem 25

Internal problem ID [16497]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 25
Date solved : Thursday, March 13, 2025 at 08:15:04 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(t),t),t)+5*diff(y(t),t) = 5*t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {t^{2}}{5}+\frac {t^{3}}{3}-\frac {{\mathrm e}^{-5 t} c_{1}}{5}+\frac {2 t}{25}+c_{2} \]

✓ Mathematica. Time used: 4.835 (sec). Leaf size: 45

ode=D[y[t],{t,2}]+5*D[y[t],t]==5*t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \int _1^te^{-5 K[2]} \left (c_1+\int _1^{K[2]}5 e^{5 K[1]} K[1]^2dK[1]\right )dK[2]+c_2 \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-5*t**2 + 5*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + C_{2} e^{- 5 t} + \frac {t^{3}}{3} - \frac {t^{2}}{5} + \frac {2 t}{25} \]