64.10.32 problem 32

Internal problem ID [13438]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 05:42:31 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([9*diff(y(x),x$2)-6*diff(y(x),x)+y(x)=0,y(0) = 3, D(y)(0) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 18

DSolve[{9*D[y[x],{x,2}]-6*D[y[x],x]+y[x]==0,{y[0]==3,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x/3} (3-2 x) \]