76.13.29 problem 29

Internal problem ID [17611]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 10:45:23 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 15

dsolve([9*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=0,y(0) = 2, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{\frac {2 x}{3}} \left (-6+7 x \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[{9*D[y[x],{x,2}]-12*D[y[x],x]+4*y[x]==0,{y[0]==2,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{2 x/3} (6-7 x) \]