73.15.20 problem 22.7 (e)

Internal problem ID [15451]
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 : 22.7 (e)
Date solved : Tuesday, January 28, 2025 at 07:56:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=(-6*x-8)*cos(2*x)+(8*x-11)*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==(-6*x-8)*Cos[2*x]+(8*x-11)*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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