73.15.66 problem 22.13 (d)

Internal problem ID [15497]
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 : 22.13 (d)
Date solved : Tuesday, January 28, 2025 at 07:59:45 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

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

\[ y = \frac {\left (30 x -98\right ) \cos \left (2 x \right )}{15}+\frac {\left (-60 x -64\right ) \sin \left (2 x \right )}{15}+\cos \left (x \right ) c_{1} +{\mathrm e}^{x} c_{2} +c_{3} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 49

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

\[ y(x)\to -4 x \sin (2 x)-\frac {64}{15} \sin (2 x)+\left (2 x-\frac {98}{15}\right ) \cos (2 x)+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]