Internal problem ID [5935]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-t \sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 25
dsolve([diff(y(t),t)+y(t)=t*sin(t),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {{\mathrm e}^{-t}}{2}+\frac {\left (1-t \right ) \cos \relax (t )}{2}+\frac {t \sin \relax (t )}{2} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 27
DSolve[{y'[t]+y[t]==t*Sin[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} (t \sin (t)-t \cos (t)+\cos (t)+\sinh (t)-\cosh (t)) \\ \end{align*}