Internal problem ID [7292]
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]]
\[ \boxed {y^{\prime \prime }+20 y^{\prime }+500 y=100000 \cos \left (100 x \right )} \]
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = {\mathrm e}^{-10 x} \sin \left (20 x \right ) c_{2} +{\mathrm e}^{-10 x} \cos \left (20 x \right ) c_{1} -\frac {3800 \cos \left (100 x \right )}{377}+\frac {800 \sin \left (100 x \right )}{377} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 47
DSolve[y''[x]+20*y'[x]+500*y[x] == 100000*Cos[100*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {200}{377} (19 \cos (100 x)-4 \sin (100 x))+c_2 e^{-10 x} \cos (20 x)+c_1 e^{-10 x} \sin (20 x) \]