73.15.67 problem 22.13 (e)

Internal problem ID [15498]
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 (e)
Date solved : Tuesday, January 28, 2025 at 07:59:46 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 42

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

\[ y = \frac {\left (-3 x^{2}+8 c_{3} +3 x +9\right ) \sin \left (x \right )}{8}+\frac {\left (-3 x^{2}+8 c_{1} -9 x \right ) \cos \left (x \right )}{8}+{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.244 (sec). Leaf size: 102

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

\[ y(x)\to e^x \int _1^x\frac {3}{2} e^{-K[3]} \cos (K[3]) K[3]dK[3]+\cos (x) \int _1^x-\frac {3}{2} \cos (K[1]) K[1] (\cos (K[1])-\sin (K[1]))dK[1]+\sin (x) \int _1^x-\frac {3}{2} \cos (K[2]) K[2] (\cos (K[2])+\sin (K[2]))dK[2]+c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]