64.11.5 problem 5

Internal problem ID [13455]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:43:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=\cos \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+4*y(x)=cos(4*x),y(x), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) c_{1} +\frac {\sin \left (4 x \right )}{26}-\frac {3 \cos \left (4 x \right )}{52} \]

✓ Solution by Mathematica

Time used: 0.464 (sec). Leaf size: 115

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+4*y[x]==Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\cos \left (\sqrt {3} x\right ) \int _1^x-\frac {e^{K[2]} \cos (4 K[2]) \sin \left (\sqrt {3} K[2]\right )}{\sqrt {3}}dK[2]+\sin \left (\sqrt {3} x\right ) \int _1^x\frac {e^{K[1]} \cos (4 K[1]) \cos \left (\sqrt {3} K[1]\right )}{\sqrt {3}}dK[1]+c_2 \cos \left (\sqrt {3} x\right )+c_1 \sin \left (\sqrt {3} x\right )\right ) \]