74.11.20 problem 32

Internal problem ID [16270]
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 : 32
Date solved : Tuesday, January 28, 2025 at 08:59:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=-256 t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 32

dsolve(diff(y(t),t$2)-6*diff(y(t),t)+8*y(t)=-256*t^3,y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 t} c_{1}}{2}-45-84 t -72 t^{2}-32 t^{3}+c_{2} {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 36

DSolve[D[y[t],{t,2}]-6*D[y[t],t]+8*y[t]==-256*t^3,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -32 t^3-72 t^2-84 t+c_1 e^{2 t}+c_2 e^{4 t}-45 \]