71.13.10 problem 10

Internal problem ID [14459]
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 : Monday, March 31, 2025 at 12:27:38 PM
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: 0.112 (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');
 

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

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

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]
 

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

✓ Sympy. Time used: 0.119 (sec). Leaf size: 27

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)
 

\[ y{\left (x \right )} = - \frac {x}{9} - \frac {11 e^{3 x}}{54} - \frac {2}{9} - \frac {31 e^{- 3 x}}{54} \]