78.12.21 problem 2 (c)

Internal problem ID [18308]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 2 (c)
Date solved : Tuesday, January 28, 2025 at 11:45:52 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 )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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) = 5],y(x), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{3 x} x \]

✓ Solution by Mathematica

Time used: 0.014 (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] == 5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^{3 x} x \]