74.11.5 problem 17

Internal problem ID [16184]
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 : 17
Date solved : Monday, March 31, 2025 at 02:46:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \left (c_1 t +c_2 \right ) {\mathrm e}^{t}+t^{2}+4 t +6 \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 26

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

\[ y(t)\to t^2+t \left (4+c_2 e^t\right )+c_1 e^t+6 \]

✓ Sympy. Time used: 0.167 (sec). Leaf size: 19

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

\[ y{\left (t \right )} = t^{2} + 4 t + \left (C_{1} + C_{2} t\right ) e^{t} + 6 \]