67.15.1 problem 22.1 (a)

Internal problem ID [16719]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.1 (a)
Date solved : Thursday, October 02, 2025 at 01:38:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+9*y(x) = 52*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 +4 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 27

ode=D[y[x],{x,2}]+9*y[x]==52*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 e^{2 x}+c_1 \cos (3 x)+c_2 \sin (3 x) \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 52*exp(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} + 4 e^{2 x} \]