7.2 problem 10

Internal problem ID [5936]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }-y-t \,{\mathrm e}^{t} \sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 17

DSolve[{y'[t]-y[t]==t*Exp[t]*Sin[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to e^t (\sin (t)-t \cos (t)) \\ \end{align*}