76.13.33 problem 33

Internal problem ID [17615]
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 : 33
Date solved : Tuesday, January 28, 2025 at 10:45:31 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 )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 11

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

\[ y = 2 \,{\mathrm e}^{-3 x} x \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 13

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

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