64.10.29 problem 29

Internal problem ID [13435]
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 : 29
Date solved : Tuesday, January 28, 2025 at 05:42:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

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