Internal problem ID [15253]
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: 483.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=-\cos \left (x \right )+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+y(x)=sin(x)-cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} -x -1\right ) \cos \left (x \right )}{2}-\frac {\sin \left (x \right ) \left (x -2 c_{2} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 31
DSolve[y''[x]+y[x]==Sin[x]-Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (-((x+1-2 c_1) \cos (x))-(x-2 c_2) \sin (x)) \]