Internal problem ID [15494]
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 18.3. Finding periodic solutions of linear
differential equations. Exercises page 187
Problem number: 757.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\cos \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+4*y(x)=cos(x)^2,y(x), singsol=all)
\[ y = \frac {\left (8 c_{1} +1\right ) \cos \left (2 x \right )}{8}+\frac {1}{8}+\frac {\left (x +8 c_{2} \right ) \sin \left (2 x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Cos[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} ((1+8 c_1) \cos (2 x)+(x+8 c_2) \sin (2 x)+1) \]