Internal problem ID [6677]
Book: Second order enumerated odes
Section: section 1
Problem number: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+\frac {x \sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 28
DSolve[y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (x \sin (x)+\cos (x)+2 c_1 \cos (x)+2 c_2 \sin (x)) \\ \end{align*}