71.13.10 problem 10

Internal problem ID [14530]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:43:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y&=x +2 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.627 (sec). Leaf size: 21

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

\[ y = -\frac {7 \cosh \left (3 x \right )}{9}+\frac {10 \sinh \left (3 x \right )}{27}-\frac {x}{9}-\frac {2}{9} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{54} e^{-3 x} \left (-6 e^{3 x} (x+2)-11 e^{6 x}-31\right ) \]