Internal problem ID [15322]
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. Superposition principle. Exercises page 137
Problem number: 553.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=x +\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-y(x)=x+sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}-\frac {\sin \left (x \right )}{2}-x \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 29
DSolve[y''[x]-y[x]==x+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x-\frac {\sin (x)}{2}+c_1 e^x+c_2 e^{-x} \]