82.30.2 problem Ex. 2

Internal problem ID [18815]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 77
Problem number : Ex. 2
Date solved : Monday, March 31, 2025 at 06:15:35 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+a^{2} y&=\cos \left (a x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)+a^2*y(x) = cos(a*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 41

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

\[ y(x)\to \frac {\left (1+4 a^2 c_1\right ) \cos (a x)+2 a (x+2 a c_2) \sin (a x)}{4 a^2} \]

✓ Sympy. Time used: 0.133 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{- i a x} + C_{2} e^{i a x} + \frac {x \sin {\left (a x \right )}}{2 a} \]