64.11.3 problem 3

Internal problem ID [13453]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:43:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=6*sin(2*x)+7*cos(2*x),y(x), singsol=all)
 

\[ y = \left (\cos \left (2 x \right ) c_{1} +\sin \left (2 x \right ) c_{2} \right ) {\mathrm e}^{-x}-\cos \left (2 x \right )+2 \sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==6*Sin[2*x]+7*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (-e^x+c_2\right ) \cos (2 x)+\left (2 e^x+c_1\right ) \sin (2 x)\right ) \]