20.21.24 problem Problem 24

Internal problem ID [3951]
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 24
Date solved : Monday, January 27, 2025 at 08:04:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.731 (sec). Leaf size: 23

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

\[ y = \frac {3 \cos \left (t \right )}{5}-\frac {4 \sin \left (t \right )}{5}-{\mathrm e}^{t}+\frac {7 \,{\mathrm e}^{2 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 29

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

\[ y(t)\to \frac {1}{5} \left (e^t \left (7 e^t-5\right )-4 \sin (t)+3 \cos (t)\right ) \]