64.10.37 problem 37

Internal problem ID [13443]
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 : 37
Date solved : Tuesday, January 28, 2025 at 05:42:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 21

dsolve([9*diff(y(x),x$2)+6*diff(y(x),x)+5*y(x)=0,y(0) = 6, D(y)(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

DSolve[{9*D[y[x],{x,2}]+6*D[y[x],x]+5*y[x]==0,{y[0]==6,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{-x/3} \left (\sin \left (\frac {2 x}{3}\right )+2 \cos \left (\frac {2 x}{3}\right )\right ) \]