75.16.16 problem 489

Internal problem ID [16918]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 489
Date solved : Monday, March 31, 2025 at 03:35:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+k^{2} y&=k \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

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

\[ y = \sin \left (k x \right ) c_2 +\cos \left (k x \right ) c_1 +\frac {1}{k} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 23

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

\[ y(x)\to c_1 \cos (k x)+c_2 \sin (k x)+\frac {1}{k} \]

✓ Sympy. Time used: 0.082 (sec). Leaf size: 22

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

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