12.19.16 problem section 9.3, problem 16

Internal problem ID [2163]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 16
Date solved : Monday, January 27, 2025 at 05:42:57 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y&=-{\mathrm e}^{x} \left (1-6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 40

dsolve(4*diff(y(x),x$4)-11*diff(y(x),x$2)-9*diff(y(x),x)-2*y(x)=-exp(x)*(1-6*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 47

DSolve[4*D[y[x],{x,4}]-11*D[y[x],{x,2}]-9*D[y[x],x]-2*y[x]==-Exp[x]*(1-6*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{3} e^x (x-1)+e^{-x/2} (c_2 x+c_1)+c_3 e^{-x}+c_4 e^{2 x} \]