Internal problem ID [14549]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+4*diff(y(t),t)=-24*t-6-4*t*exp(-4*t)+exp(-4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (2 t^{2}-c_{1} \right ) {\mathrm e}^{-4 t}}{4}-3 t^{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.24 (sec). Leaf size: 32
DSolve[y''[t]+4*y'[t]==-24*t-6-4*t*Exp[-4*t]+Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -3 t^2+\frac {1}{4} e^{-4 t} \left (2 t^2-c_1\right )+c_2 \]