8.9.11 problem 22

Internal problem ID [855]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 22
Date solved : Wednesday, February 05, 2025 at 04:42:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 31

dsolve([9*diff(y(x),x$2)+6*diff(y(x),x)+4*y(x)=0,y(0) = 3, D(y)(0) = 4],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{3}} \left (5 \sqrt {3}\, \sin \left (\frac {\sqrt {3}\, x}{3}\right )+3 \cos \left (\frac {\sqrt {3}\, x}{3}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 39

DSolve[{9*D[y[x],{x,2}]+6*D[y[x],x]+4*y[x]==0,{y[0]==3,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/3} \left (5 \sqrt {3} \sin \left (\frac {x}{\sqrt {3}}\right )+3 \cos \left (\frac {x}{\sqrt {3}}\right )\right ) \]