Internal problem ID [5923]
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. 7.3.1 TRANSLATION ON THE s-AXIS. Page
297
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y-{\mathrm e}^{t} \cos \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)-y(t)=exp(t)*cos(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (-\cos \relax (t )+2 \sin \relax (t )\right ) {\mathrm e}^{t}}{5}+\frac {{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 27
DSolve[{y''[t]-y[t]==Exp[t]*Cos[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{5} \left (e^{-t}-e^t (\cos (t)-2 \sin (t))\right ) \\ \end{align*}