74.11.18 problem 30

Internal problem ID [16268]
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 : 30
Date solved : Tuesday, January 28, 2025 at 08:59:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=-32 t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

dsolve(diff(y(t),t$2)+3*diff(y(t),t)-4*y(t)=-32*t^2,y(t), singsol=all)
 

\[ y = \left (8 t^{2}+12 t +13\right ) {\mathrm e}^{-4 t} {\mathrm e}^{4 t}+\left (c_{1} {\mathrm e}^{5 t}+c_{2} \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 29

DSolve[D[y[t],{t,2}]+3*D[y[t],t]-4*y[t]==-32*t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 8 t^2+12 t+c_1 e^{-4 t}+c_2 e^t+13 \]