14.17.4 problem 22

Internal problem ID [2682]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.10, Some useful properties of Laplace transform. Excercises page 238
Problem number : 22
Date solved : Monday, January 27, 2025 at 06:06:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+7 y&=\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 \end{align*}

✓ Solution by Maple

Time used: 0.995 (sec). Leaf size: 36

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

\[ y = -\frac {{\mathrm e}^{t} \sqrt {6}\, \sin \left (\sqrt {6}\, t \right )}{60}-\frac {{\mathrm e}^{t} \cos \left (\sqrt {6}\, t \right )}{20}+\frac {3 \sin \left (t \right )}{20}+\frac {\cos \left (t \right )}{20} \]

✓ Solution by Mathematica

Time used: 0.869 (sec). Leaf size: 49

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

\[ y(t)\to \frac {1}{60} \left (9 \sin (t)-\sqrt {6} e^t \sin \left (\sqrt {6} t\right )+3 \cos (t)-3 e^t \cos \left (\sqrt {6} t\right )\right ) \]