Internal problem ID [617]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = \alpha , y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(x),x$2) -diff(y(x),x)-2*y(x) = 0,y(0) = alpha, D(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\alpha +2\right ) {\mathrm e}^{2 x}}{3}+\frac {2 \,{\mathrm e}^{-x} \left (\alpha -1\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 29
DSolve[{y''[x]-y'[x]-2*y[x]==0,{y[0]==\[Alpha],y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x} \left (2 (\alpha -1)+(\alpha +2) e^{3 x}\right ) \\ \end{align*}