88.22.10 problem 14

Internal problem ID [24170]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 160 (Laplace transform)
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:00:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=3 x -6 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{3}} \\ y^{\prime }\left (0\right )&={\frac {4}{3}} \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+9*y(x) = 3*x-6; 
ic:=[y(0) = 1/3, D(y)(0) = 4/3]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+9*y[x]==3*x-6; 
ic={y[0]==1/3,Derivative[1][y][0] ==4/3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} (x+\sin (3 x)+3 \cos (3 x)-2) \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + 9*y(x) + Derivative(y(x), (x, 2)) + 6,0) 
ics = {y(0): 1/3, Subs(Derivative(y(x), x), x, 0): 4/3} 
dsolve(ode,func=y(x),ics=ics)
 

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