73.15.60 problem 22.12 (e)

Internal problem ID [15491]
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 (e)
Date solved : Tuesday, January 28, 2025 at 07:59:42 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 30

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

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