Internal problem ID [15176]
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 13. Basic concepts and definitions. Exercises
page 98
Problem number: 318.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=2 \cos \left (x \right )+2 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+y(x)=2*(cos(x)+sin(x)),y(x), singsol=all)
\[ y = \left (c_{1} -x +1\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x +c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==2*(Cos[x]+Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-x+1+c_1) \cos (x)+(x+c_2) \sin (x) \]