Internal problem ID [14903]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 5. Applications of Higher Order Equations. Exercises 5.2, page 241
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+4 x^{\prime }+3 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(x(t),t$2)+4*diff(x(t),t)+3*x(t)=0,x(0) = 0, D(x)(0) = -4],x(t), singsol=all)
\[ x \left (t \right ) = 2 \,{\mathrm e}^{-3 t}-2 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 19
DSolve[{x''[t]+4*x'[t]+3*x[t]==0,{x[0]==0,x'[0]==-4}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -2 e^{-3 t} \left (e^{2 t}-1\right ) \]