67.17.32 problem 32

Internal problem ID [16853]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 32
Date solved : Thursday, October 02, 2025 at 01:39:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = 25*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{6 x}+\frac {4 \cos \left (3 x \right )}{9}+\frac {\sin \left (3 x \right )}{3} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 35

ode=D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==25*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} \sin (3 x)+\frac {4}{9} \cos (3 x)+e^{6 x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 25*sin(3*x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{6 x} + \frac {\sin {\left (3 x \right )}}{3} + \frac {4 \cos {\left (3 x \right )}}{9} \]