67.15.8 problem 22.3 (c)

Internal problem ID [16726]
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 : 22.3 (c)
Date solved : Thursday, October 02, 2025 at 01:38:13 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x) = 26*cos(1/3*x)-12*sin(1/3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-3 x} c_1}{3}+27 \sin \left (\frac {x}{3}\right )+9 \cos \left (\frac {x}{3}\right )+c_2 \]

✓ Mathematica. Time used: 4.38 (sec). Leaf size: 60

ode=D[y[x],{x,2}]+3*D[y[x],x]==26*Cos[x/3]-12*Sin[x/3]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^xe^{-3 K[2]} \left (c_1+\int _1^{K[2]}2 e^{3 K[1]} \left (13 \cos \left (\frac {K[1]}{3}\right )-6 \sin \left (\frac {K[1]}{3}\right )\right )dK[1]\right )dK[2]+c_2 \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*sin(x/3) - 26*cos(x/3) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 3 x} + 27 \sin {\left (\frac {x}{3} \right )} + 9 \cos {\left (\frac {x}{3} \right )} \]