12.19.13 problem section 9.3, problem 13

Internal problem ID [2160]
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 13
Date solved : Monday, January 27, 2025 at 05:42:56 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y&=-3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 40

dsolve(diff(y(x),x$4)+3*diff(y(x),x$3)-3*diff(y(x),x$2)-7*diff(y(x),x)+6*y(x)=-3*exp(-x)*(12+8*x-8*x^2),y(x), singsol=all)
 

\[ y = 3 \left (\left (x -1\right )^{2} {\mathrm e}^{2 x}+\frac {\left (c_4 x +c_1 \right ) {\mathrm e}^{4 x}}{3}+\frac {c_3 \,{\mathrm e}^{x}}{3}+\frac {c_2}{3}\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 45

DSolve[D[y[x],{x,4}]+3*D[y[x],{x,3}]-3*D[y[x],{x,2}]-7*D[y[x],x]+6*y[x]==-3*Exp[-x]*(12+8*x-8*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (3 e^{2 x} (x-1)^2+c_2 e^x+e^{4 x} (c_4 x+c_3)+c_1\right ) \]