Internal problem ID [666]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 14.
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 }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 2, y^{\prime }\left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(y(x),x$2)+4*diff(y(x),x)+4*y(x) = 0,y(-1) = 2, D(y)(-1) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2-2 x} \left (5 x +7\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[{y''[x]+4*y'[x]+4*y[x]==0,{y[-1]==2,y'[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 (x+1)} (5 x+7) \\ \end{align*}