Internal problem ID [2311]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }-k^{2} x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = v_{0}] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(x(t),t$2)-k^2*x(t)=0,x(0) = 0, D(x)(0) = v__0],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {v_{0} \left ({\mathrm e}^{-k t}-{\mathrm e}^{k t}\right )}{2 k} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 27
DSolve[{x''[t]-k^2*x[t]==0,{x[0]==0,x'[0]==v0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {\text {v0} e^{-k t} \left (e^{2 k t}-1\right )}{2 k} \]