Internal problem ID [11448]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.2.2 Real eigenvalues. Exercises page
90
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([1/2*diff(x(t),t$2)+diff(x(t),t)+1/2*x(t)=0,x(0) = 1, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} \left (t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 14
DSolve[{1/2*x''[t]+x'[t]+1/2*x[t]==0,{x[0]==1,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-t} (t+1) \]