Internal problem ID [14854]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+12 y=3 t^{2} {\mathrm e}^{-4 t}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = \left (-t^{3}-3 t^{2}+c_{1} -6 t \right ) {\mathrm e}^{-4 t}+c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 34
DSolve[y''[t]+7*y'[t]+12*y[t]==3*t^2*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} \left (-t^3-3 t^2-6 t+c_2 e^t-6+c_1\right ) \]