Internal problem ID [634]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)+ 4*diff(y(x),x)+5*y(x) = 0,y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} \left (2 \sin \relax (x )+\cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]+4*y'[x]+5*y[x]==0,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} (2 \sin (x)+\cos (x)) \\ \end{align*}