Internal problem ID [14905]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = -{\frac {1}{2}}, x^{\prime }\left (0\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 39
dsolve([1/4*diff(x(t),t$2)+2*diff(x(t),t)+x(t)=0,x(0) = -1/2, D(x)(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (-3-\sqrt {3}\right ) {\mathrm e}^{2 \left (-2+\sqrt {3}\right ) t}}{12}+\frac {{\mathrm e}^{-2 \left (2+\sqrt {3}\right ) t} \left (\sqrt {3}-3\right )}{12} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 47
DSolve[{1/4*x''[t]+2*x'[t]+x[t]==0,{x[0]==-1/2,x'[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{12} e^{-2 \left (2+\sqrt {3}\right ) t} \left (-\left (3+\sqrt {3}\right ) e^{4 \sqrt {3} t}-3+\sqrt {3}\right ) \]