Internal problem ID [5199]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 52
Problem number: 2(b).
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 }-6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)+diff(y(x),x)-6*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left ({\mathrm e}^{5 x}-1\right ) {\mathrm e}^{-3 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y''[x]+y'[x]-6*y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^{-3 x} \left (e^{5 x}-1\right ) \\ \end{align*}