67.15.40 problem 22.10 (m)

Internal problem ID [16758]
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 : 22.10 (m)
Date solved : Thursday, October 02, 2025 at 01:38:33 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)+y(x) = 6*cos(x)-3*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_1 +3 x +6\right ) \cos \left (x \right )}{2}+3 \left (x +\frac {c_2}{3}\right ) \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.342 (sec). Leaf size: 66

ode=D[y[x],{x,2}]+y[x]==6*Cos[x]-3*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \cos (x) \int _1^x3 \sin (K[1]) (\sin (K[1])-2 \cos (K[1]))dK[1]+\sin (x) \int _1^x3 \cos (K[2]) (2 \cos (K[2])-\sin (K[2]))dK[2]+c_1 \cos (x)+c_2 \sin (x) \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 3*sin(x) - 6*cos(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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