Internal problem ID [641]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = \alpha ] \end {align*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 32
dsolve([diff(y(x),x$2)+ 2*diff(y(x),x)+6*y(x) = 0,y(0) = 2, D(y)(0) = alpha],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x} \left (\sqrt {5}\, \left (\alpha +2\right ) \sin \left (\sqrt {5}\, x \right )+10 \cos \left (\sqrt {5}\, x \right )\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[{y''[x]+2*y'[x]+6*y[x]==0,{y[0]==2,y'[0]==\[Alpha]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^{-x} \left (\sqrt {5} (\alpha +2) \sin \left (\sqrt {5} x\right )+10 \cos \left (\sqrt {5} x\right )\right ) \\ \end{align*}