Internal problem ID [14617]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-16 y=16 t \,{\mathrm e}^{-4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 29
dsolve([diff(y(t),t$2)-16*y(t)=16*t*exp(-4*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-32 t^{2}-8 t -1\right ) {\mathrm e}^{-4 t}}{32}+\frac {{\mathrm e}^{4 t}}{32} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 29
DSolve[{y''[t]-16*y[t]==16*t*Exp[-4*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{32} e^{-4 t} \left (-32 t^2-8 t+e^{8 t}-1\right ) \]