Internal problem ID [630]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime }+9 y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(9*diff(y(x),x$2) +9*diff(y(x),x)-4*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x}{3}}+c_{2} {\mathrm e}^{-\frac {4 x}{3}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[9*y''[x]+9*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-4 x/3} \left (c_2 e^{5 x/3}+c_1\right ) \\ \end{align*}