7.11.14 problem 14

Internal problem ID [335]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:45:43 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.215 (sec). Leaf size: 35

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

\[ y = \left (c_4 x +c_2 \right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{x} \left (x^{3}+24 x c_3 -3 x^{2}+24 c_1 \right )}{24} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 50

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

\[ y(x)\to \frac {1}{48} e^x \left (2 x^3-6 x^2+(9+48 c_4) x-6+48 c_3\right )+e^{-x} (c_2 x+c_1) \]