74.18.27 problem 33

Internal problem ID [16584]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 09:11:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=3 t^{2} {\mathrm e}^{-4 t} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

dsolve(diff(y(t),t$2)+7*diff(y(t),t)+12*y(t)=3*t^2*exp(-4*t),y(t), singsol=all)
 

\[ y = \left (-t^{3}-3 t^{2}+c_{1} -6 t \right ) {\mathrm e}^{-4 t}+{\mathrm e}^{-3 t} c_{2} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 48

DSolve[D[y[t],{t,2}]+7*D[y[t],t]+12*y[t]==3*t^2*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (e^t \int _1^t3 e^{-K[1]} K[1]^2dK[1]-t^3+c_2 e^t+c_1\right ) \]