20.21.11 problem Problem 11

Internal problem ID [3938]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 11
Date solved : Monday, January 27, 2025 at 08:04:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=36 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 2.544 (sec). Leaf size: 12

dsolve([diff(y(t),t$2)-diff(y(t),t)-12*y(t)=36,y(0) = 0, D(y)(0) = 12],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{4 t}-3 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

DSolve[{D[y[t],{t,2}]-D[y[t],t]-12*y[t]==36,{y[0]==0,Derivative[1][y][0] ==12}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 \left (e^{4 t}-1\right ) \]