73.10.16 problem 15.6 (c)

Internal problem ID [15311]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.6 (c)
Date solved : Tuesday, January 28, 2025 at 07:52:12 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=-24 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)-10*diff(y(x),x)+9*y(x)=0,y(0) = 8, D(y)(0) = -24],y(x), singsol=all)
 

\[ y = 12 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{9 x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]-10*D[y[x],x]+9*y[x]==0,{y[0]==8,Derivative[1][y][0] ==-24}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -4 e^x \left (e^{8 x}-3\right ) \]