Internal problem ID [14904]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 39
dsolve([1/32*diff(x(t),t$2)+2*diff(x(t),t)+x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\left (31+4 \sqrt {62}\right ) {\mathrm e}^{4 \left (-8+\sqrt {62}\right ) t}}{62}+\frac {\left (31-4 \sqrt {62}\right ) {\mathrm e}^{-4 \left (8+\sqrt {62}\right ) t}}{62} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 50
DSolve[{1/32*x''[t]+2*x'[t]+x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{62} e^{-4 \left (8+\sqrt {62}\right ) t} \left (\left (31+4 \sqrt {62}\right ) e^{8 \sqrt {62} t}+31-4 \sqrt {62}\right ) \]