52.7.1 problem 9

Internal problem ID [8356]
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 : 9
Date solved : Monday, January 27, 2025 at 03:49:28 PM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.585 (sec). Leaf size: 25

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

\[ y = -\frac {{\mathrm e}^{-t}}{2}+\frac {\left (1-t \right ) \cos \left (t \right )}{2}+\frac {t \sin \left (t \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 28

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

\[ y(t)\to \frac {1}{2} \left (-e^{-t}+t \sin (t)-t \cos (t)+\cos (t)\right ) \]