Internal problem ID [656]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }+12 y^{\prime }+9 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(4*diff(y(x),x$2)+12*diff(y(x),x)+9*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {3 x}{2}} \left (c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 20
DSolve[4*y''[x]+12*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x/2} (c_2 x+c_1) \]