9.2.4 problem problem 13

Internal problem ID [938]
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
Date solved : Monday, January 27, 2025 at 03:22:36 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: 0.026 (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]
 

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