Internal problem ID [15380]
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. Initial value problem. Exercises page 140
Problem number: 611.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=-2 \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)-y(x)=-2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 22
DSolve[y''[x]-y[x]==-2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x)+c_1 e^x+c_2 e^{-x} \]