Internal problem ID [655]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-4 y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(4*diff(y(x),x$2)-4*diff(y(x),x)-3*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[4*y''[x]-4*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/2} \left (c_2 e^{2 x}+c_1\right ) \\ \end{align*}