Internal problem ID [622]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant
Coefficients, page 144
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = \beta ] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 23
dsolve([diff(y(x),x$2) +5*diff(y(x),x)+6*y(x) = 0,y(0) = 2, D(y)(0) = beta],y(x), singsol=all)
\[ y \relax (x ) = \left (-4-\beta \right ) {\mathrm e}^{-3 x}+\left (\beta +6\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[{y''[x]+5*y'[x]+6*y[x]==0,{y[0]==2,y'[0]==\[Beta]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (-\beta +(\beta +6) e^x-4\right ) \\ \end{align*}