74.11.5 problem 17

Internal problem ID [16255]
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 : Tuesday, January 28, 2025 at 08:58:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(t),t$2)-2*diff(y(t),t)+y(t)=t^2,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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