73.15.62 problem 22.12 (g)

Internal problem ID [15493]
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 (g)
Date solved : Tuesday, January 28, 2025 at 07:59:43 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=6*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==6*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (3 x-3+c_3)+c_1 \cos (x)+c_2 \sin (x) \]