71.13.11 problem 11

Internal problem ID [14531]
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 : 11
Date solved : Tuesday, January 28, 2025 at 06:43:02 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: 9.511 (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)
 

\[ y = -\frac {11 \cos \left (3 x \right )}{9}+\frac {8 \sin \left (3 x \right )}{27}+\frac {x}{9}+\frac {2}{9} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{27} (3 x+8 \sin (3 x)-33 \cos (3 x)+6) \]