52.7.2 problem 10

Internal problem ID [8357]
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 : 10
Date solved : Monday, January 27, 2025 at 03:49:29 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=t \,{\mathrm e}^{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: 0.680 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 17

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

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