Internal problem ID [5756]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 7. Laplace Transforms. Section 7.5 Problesm for review and discovery. Section A,
Drill exercises. Page 309
Problem number: 4(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[y''[t]-5*y'[t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (c_2 e^{3 t}+c_1\right ) \\ \end{align*}