73.15.61 problem 22.12 (f)

Internal problem ID [15492]
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 : 22.12 (f)
Date solved : Tuesday, January 28, 2025 at 07:59:42 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=30*cos(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==30*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -4 \sin (2 x)+2 \cos (2 x)+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]