73.15.68 problem 22.13 (f)

Internal problem ID [15499]
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 (f)
Date solved : Tuesday, January 28, 2025 at 07:59:47 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \,{\mathrm e}^{x} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 37

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

\[ y = \frac {\left (\left (-30 x +57\right ) \cos \left (x \right )+\left (15 x +24\right ) \sin \left (x \right )+25 c_{2} \right ) {\mathrm e}^{x}}{25}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 49

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

\[ y(x)\to c_3 e^x+\left (e^x \left (\frac {57}{25}-\frac {6 x}{5}\right )+c_1\right ) \cos (x)+\left (\frac {3}{25} e^x (5 x+8)+c_2\right ) \sin (x) \]