73.14.5 problem 21.7

Internal problem ID [15415]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.7
Date solved : Tuesday, January 28, 2025 at 07:54:55 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y&=36 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)-9*y(x)=36,y(0) = 8, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{-3 x}+7 \,{\mathrm e}^{3 x}-4 \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

DSolve[{D[y[x],{x,2}]-9*y[x]==36,{y[0]==8,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^{-3 x}+7 e^{3 x}-4 \]