73.15.69 problem 22.13 (g)

Internal problem ID [15500]
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 (g)
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&=5 x^{5} {\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 48

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=5*x^5*exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (625 x^{5}-5625 x^{4}+28000 x^{3}-91200 x^{2}+187320 x -188376\right ) {\mathrm e}^{2 x}}{625}+\cos \left (x \right ) c_{1} +{\mathrm e}^{x} c_{2} +c_{3} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 58

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==5*x^5*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (e^x \left (x^5-9 x^4+\frac {224 x^3}{5}-\frac {3648 x^2}{25}+\frac {37464 x}{125}-\frac {188376}{625}\right )+c_3\right )+c_1 \cos (x)+c_2 \sin (x) \]