Internal problem ID [7433]
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]]
\[ \boxed {y^{\prime \prime }+y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\frac {x \sin \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 28
DSolve[y''[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (x \sin (x)+\cos (x)+2 c_1 \cos (x)+2 c_2 \sin (x)) \]