Internal problem ID [288]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 13.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(9*diff(y(x),x$3)+12*diff(y(x),x$2)+4*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{-\frac {2 x}{3}}+c_{3} {\mathrm e}^{-\frac {2 x}{3}} x \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 32
DSolve[9*y'''[x]+12*y''[x]+4*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3-\frac {3}{4} e^{-2 x/3} (c_2 (2 x+3)+2 c_1) \\ \end{align*}