75.18.22 problem 611

Internal problem ID [17110]
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. Initial value problem. Exercises page 140
Problem number : 611
Date solved : Tuesday, January 28, 2025 at 09:53:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-y(x)=-2*cos(x),y(x), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} +\cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]-y[x]==-2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x)+c_1 e^x+c_2 e^{-x} \]