64.20.11 problem 11

Internal problem ID [13654]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 05:54:22 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 8.266 (sec). Leaf size: 19

dsolve([diff(y(t),t$3)-5*diff(y(t),t$2)+7*diff(y(t),t)-3*y(t)=20*sin(t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = -2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 21

DSolve[{D[y[t],{t,3}]-5*D[y[t],{t,2}]+7*D[y[t],t]-3*y[t]==20*Sin[t],{y[0]==0,Derivative[1][y][0]==0,Derivative[2][y][0]==-2}},{y[t]},t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t (3-4 t)+\sin (t)-3 \cos (t) \]