8.7.24 problem 40

Internal problem ID [830]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 40
Date solved : Monday, January 27, 2025 at 03:09:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 20

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

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