65.14.4 problem 10

Internal problem ID [15825]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:28:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ y^{\prime }\left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.114 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+9*y(x) = 18*exp(3*x); 
ic:=[y(0) = -1, D(y)(0) = 6]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

ode=D[y[x],{x,2}]+9*y[x]==18*Exp[3*x]; 
ic={y[0]==-1,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.047 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 18*exp(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

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