Internal problem ID [15259]
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 ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 489.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+k^{2} y=k} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+k^2*y(x)=k,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (k x \right ) c_{2} +\cos \left (k x \right ) c_{1} +\frac {1}{k} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 23
DSolve[y''[x]+k^2*y[x]==k,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (k x)+c_2 \sin (k x)+\frac {1}{k} \]