20.7.15 problem Problem 40

Internal problem ID [3730]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 40
Date solved : Monday, January 27, 2025 at 07:56:48 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=4 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+y(x)=4*x*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \cos \left (x \right ) c_{1} +c_{2} \sin \left (x \right )+c_3 \,{\mathrm e}^{-x}+x \,{\mathrm e}^{x}-\frac {3 \,{\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 36

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]+D[y[x],x]+y[x]==4*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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