50.25.1 problem 3(a)

Internal problem ID [8173]
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 : 3(a)
Date solved : Monday, January 27, 2025 at 03:45:13 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-5 y&=1 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.727 (sec). Leaf size: 35

dsolve([diff(y(t),t$2)+3*diff(y(t),t)-5*y(t)=1,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {13 \sqrt {29}\, \sinh \left (\frac {t \sqrt {29}}{2}\right ) {\mathrm e}^{-\frac {3 t}{2}}}{145}+\frac {\cosh \left (\frac {t \sqrt {29}}{2}\right ) {\mathrm e}^{-\frac {3 t}{2}}}{5}-\frac {1}{5} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 67

DSolve[{D[y[t],{t,2}]+3*D[y[t],t]-5*y[t]==1,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{290} e^{-\frac {1}{2} \left (3+\sqrt {29}\right ) t} \left (\left (29+13 \sqrt {29}\right ) e^{\sqrt {29} t}-58 e^{\frac {1}{2} \left (3+\sqrt {29}\right ) t}+29-13 \sqrt {29}\right ) \]