20.21.13 problem Problem 13

Internal problem ID [3940]
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 13
Date solved : Monday, January 27, 2025 at 08:04:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\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: 2.647 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=4*exp(3*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{t}+2 \,{\mathrm e}^{3 t}-4 \,{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 17

DSolve[{D[y[t],{t,2}]-3*D[y[t],t]+2*y[t]==4*Exp[3*t],{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^t \left (e^t-1\right )^2 \]