Internal problem ID [14518]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+3 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = a, y^{\prime }\left (0\right ) = b] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve([diff(y(t),t$2)+4*diff(y(t),t)+3*y(t)=0,y(0) = a, D(y)(0) = b],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-a -b \right ) {\mathrm e}^{-3 t}}{2}+\frac {3 \left (a +\frac {b}{3}\right ) {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 35
DSolve[{y''[t]+4*y'[t]+3*y[t]==0,{y[0]==a,y'[0]==b}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-3 t} \left (a \left (3 e^{2 t}-1\right )+b \left (e^{2 t}-1\right )\right ) \]