74.11.28 problem 40

Internal problem ID [16278]
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 : 40
Date solved : Tuesday, January 28, 2025 at 09:00:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 39

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

\[ y = \frac {\left (-t^{4}+4 t^{3}-12 t^{2}+2 c_{1} +24 t \right ) {\mathrm e}^{4 t}}{2}+c_{2} {\mathrm e}^{3 t} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 42

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

\[ y(t)\to e^{3 t} \left (e^t \left (-\frac {t^4}{2}+2 t^3-6 t^2+12 t-12+c_2\right )+c_1\right ) \]