Internal problem ID [6509]
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]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 1.687 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{\frac {5 t}{2}} \left (3 y \left (0\right ) \cosh \left (\frac {3 t}{2}\right )+\sinh \left (\frac {3 t}{2}\right ) \left (2 D\left (y \right )\left (0\right )-5 y \left (0\right )\right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 20
DSolve[y''[t]-5*y'[t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (c_2 e^{3 t}+c_1\right ) \]