Internal problem ID [14563]
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: 57.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=-24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)+4*diff(y(t),t)=-24*t-6-4*t*exp(-4*t)+exp(-4*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2} \left (-6+{\mathrm e}^{-4 t}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 19
DSolve[{y''[t]+4*y'[t]==-24*t-6-4*t*Exp[-4*t]+Exp[-4*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} \left (e^{-4 t}-6\right ) t^2 \]