Internal problem ID [6667]
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. 7.2.2 TRANSFORMS OF
DERIVATIVES Page 289
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 1.765 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+5*y(t)=0,y(0) = 1, D(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t} \left (\cos \left (2 t \right )+\sin \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 18
DSolve[{y''[t]-2*y'[t]+5*y[t]==0,{y[0]==1,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t (\sin (2 t)+\cos (2 t)) \]