Internal problem ID [14625]
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: 58 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime }+4 y^{\prime }+y={\mathrm e}^{-\frac {t}{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = a, y^{\prime }\left (0\right ) = b] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve([4*diff(y(t),t$2)+4*diff(y(t),t)+y(t)=exp(-t/2),y(0) = a, D(y)(0) = b],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\frac {t^{2}}{4}+t \left (a +2 b \right )+2 a \right ) {\mathrm e}^{-\frac {t}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 30
DSolve[{4*y''[t]+4*y'[t]+y[t]==Exp[-t/2],{y[0]==a,y'[0]==b}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} e^{-t/2} (4 a (t+2)+t (8 b+t)) \]