78.12.24 problem 2 (f)

Internal problem ID [18311]
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 (f)
Date solved : Tuesday, January 28, 2025 at 11:45:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)+8*diff(y(x),x)-9*y(x)=0,y(1) = 2, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{9-9 x}}{5}+\frac {9 \,{\mathrm e}^{x -1}}{5} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

DSolve[{D[y[x],{x,2}] +8*D[y[x],x]-9*y[x]==0,{y[1]==2,Derivative[1][y][1] == 0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{9-9 x}+\frac {9 e^{x-1}}{5} \]