15.11.21 problem 21

Internal problem ID [3131]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 21
Date solved : Monday, January 27, 2025 at 07:22:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=5 \cos \left (6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 53

dsolve(diff(y(x),x$2)+2*n*diff(y(x),x)+n^2*y(x)=5*cos(6*x),y(x), singsol=all)
 

\[ y = \frac {\left (n^{2}+36\right )^{2} \left (c_{1} x +c_2 \right ) {\mathrm e}^{-n x}+5 \cos \left (6 x \right ) n^{2}+60 \sin \left (6 x \right ) n -180 \cos \left (6 x \right )}{\left (n^{2}+36\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 57

DSolve[D[y[x],{x,2}]+2*n*D[y[x],{x,2}]+n^2*y[x]==5*Cos[6*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 \cos (6 x)}{n^2-72 n-36}+c_1 e^{\frac {n x}{\sqrt {-2 n-1}}}+c_2 e^{-\frac {n x}{\sqrt {-2 n-1}}} \]