71.13.11 problem 11

Internal problem ID [14452]
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 : Thursday, March 13, 2025 at 03:30:42 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*}

✓ Maple. Time used: 9.511 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+9*y(x) = x+2; 
ic:=y(0) = -1, D(y)(0) = 1; 
dsolve([ode,ic],y(x),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + 9*y(x) + Derivative(y(x), (x, 2)) - 2,0) 
ics = {y(0): -1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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