74.11.27 problem 39

Internal problem ID [16277]
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 : 39
Date solved : Tuesday, January 28, 2025 at 09:00:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 31

dsolve(diff(y(t),t$2)-4*diff(y(t),t)-5*y(t)=-648*t^2*exp(5*t),y(t), singsol=all)
 

\[ y = \left (-36 t^{3}+18 t^{2}+c_{2} -6 t \right ) {\mathrm e}^{5 t}+{\mathrm e}^{-t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 47

DSolve[D[y[t],{t,2}]-4*D[y[t],t]-5*y[t]==-648*t^2*Exp[5*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (\int _1^t108 e^{6 K[1]} K[1]^2dK[1]+e^{6 t} \left (-36 t^3+c_2\right )+c_1\right ) \]