7.10.13 problem 13

Internal problem ID [283]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 13
Date solved : Monday, January 27, 2025 at 02:43:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(9*diff(y(x),x$3)+12*diff(y(x),x$2)+4*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \left (x c_3 +c_2 \right ) {\mathrm e}^{-\frac {2 x}{3}}+c_1 \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 32

DSolve[9*D[y[x],{x,3}]+12*D[y[x],{x,2}]+4*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3-\frac {3}{4} e^{-2 x/3} (c_2 (2 x+3)+2 c_1) \]