Internal problem ID [7419]
Book: Second order enumerated odes
Section: section 1
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.63 (sec). Leaf size: 50
DSolve[y''[x]+y'[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sin (x)+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]