Internal problem ID [6539]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 68.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+20 y^{\prime }+500 y-100000 \cos \left (100 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 37
dsolve(diff(diff(y(x),x),x)+20*diff(y(x),x)+500*y(x) = 100000*cos(100*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-10 x} \sin \left (20 x \right ) c_{2}+{\mathrm e}^{-10 x} \cos \left (20 x \right ) c_{1}-\frac {3800 \cos \left (100 x \right )}{377}+\frac {800 \sin \left (100 x \right )}{377} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 44
DSolve[y''[x]+20*y'[x]+500*y[x] == 100000*Cos[100*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {200}{377} (19 \cos (100 x)-4 \sin (100 x))+e^{-10 x} (c_2 \cos (20 x)+c_1 \sin (20 x)) \\ \end{align*}