52.7.9 problem 36

Internal problem ID [8364]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.4.1 DERIVATIVES OF A TRANSFORM. Page 309
Problem number : 36
Date solved : Monday, January 27, 2025 at 03:49:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sin \left (t \right )+t \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: 0.610 (sec). Leaf size: 17

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

\[ y = \frac {\left (\sin \left (t \right )-t \cos \left (t \right )\right ) \left (t +2\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 21

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

\[ y(t)\to -\frac {1}{4} (t+2) (t \cos (t)-\sin (t)) \]