74.11.30 problem 42

Internal problem ID [16280]
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 : 42
Date solved : Tuesday, January 28, 2025 at 09:00:14 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)-3*diff(y(t),t)=t^2-exp(3*t),y(t), singsol=all)
 

\[ y = \frac {\left (1-3 t +3 c_{1} \right ) {\mathrm e}^{3 t}}{9}-\frac {t^{3}}{9}-\frac {t^{2}}{9}-\frac {2 t}{27}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.567 (sec). Leaf size: 46

DSolve[D[y[t],{t,2}]-3*D[y[t],t]==t^2-Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

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