50.24.1 problem 1(a)

Internal problem ID [8167]
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 The Unit Step and Impulse Functions. Page 303
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:45:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.660 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+6*y(t)=5*exp(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 26

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+6*y[t]==5*Exp[3*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} e^{-3 t} \left (-6 e^t+e^{6 t}+5\right ) \]