Internal problem ID [14558]
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: 52.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y=t \,{\mathrm e}^{-t}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {5}{16}}, y^{\prime }\left (0\right ) = {\frac {9}{16}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=t*exp(-t),y(0) = -5/16, D(y)(0) = 9/16],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (4 t -5\right ) {\mathrm e}^{-t}}{16} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 19
DSolve[{y''[t]+7*y'[t]+10*y[t]==t*Exp[-t],{y[0]==-15/48,y'[0]==9/16}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{16} e^{-t} (4 t-5) \]