73.15.41 problem 22.10 (n)

Internal problem ID [15472]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (n)
Date solved : Tuesday, January 28, 2025 at 07:57:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+y(x)=6*cos(2*x)-3*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]+y[x]==6*Cos[2*x]-3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (2 x)-2 \cos (2 x)+c_1 \cos (x)+c_2 \sin (x) \]