50.25.5 problem 4(a)

Internal problem ID [8177]
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)
Date solved : Monday, January 27, 2025 at 03:45:16 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method

✓ Solution by Maple

Time used: 0.619 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)-5*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {5 t}{2}} \left (3 y \left (0\right ) \cosh \left (\frac {3 t}{2}\right )+\sinh \left (\frac {3 t}{2}\right ) \left (2 y^{\prime }\left (0\right )-5 y \left (0\right )\right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[D[y[t],{t,2}]-5*D[y[t],t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (c_2 e^{3 t}+c_1\right ) \]