Internal problem ID [6676]
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]]
\[ \boxed {y^{\prime \prime }-y={\mathrm e}^{t} \cos \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 2.0 (sec). Leaf size: 24
dsolve([diff(y(t),t$2)-y(t)=exp(t)*cos(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{-t}}{5}+\frac {{\mathrm e}^{t} \left (-\cos \left (t \right )+2 \sin \left (t \right )\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 29
DSolve[{y''[t]-y[t]==Exp[t]*Cos[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{5} \left (e^{-t}+2 e^t \sin (t)-e^t \cos (t)\right ) \]