75.5.9 problem 9

Internal problem ID [19957]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 9
Date solved : Thursday, October 02, 2025 at 05:04:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+y(x) = cos(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to \frac {1}{2} (x \sin (x)+\cos (x)+2 c_1 \cos (x)+2 c_2 \sin (x)) \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 15

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

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