56.4.71 problem 68

Internal problem ID [8960]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 68
Date solved : Monday, January 27, 2025 at 05:20:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.065 (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)
 

\[ y = {\mathrm e}^{-10 x} \sin \left (20 x \right ) c_{2} +{\mathrm e}^{-10 x} \cos \left (20 x \right ) c_{1} -\frac {3800 \cos \left (100 x \right )}{377}+\frac {800 \sin \left (100 x \right )}{377} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]+20*D[y[x],x]+500*y[x] == 100000*Cos[100*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {200}{377} (19 \cos (100 x)-4 \sin (100 x))+c_2 e^{-10 x} \cos (20 x)+c_1 e^{-10 x} \sin (20 x) \]