12.19.2 problem section 9.3, problem 2

Internal problem ID [2149]
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 2
Date solved : Monday, January 27, 2025 at 05:42:50 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-3 x} \left (6 x^{2}-23 x +32\right ) \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(-3*x)*(32-23*x+6*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (4 c_3 \,{\mathrm e}^{6 x}+4 \,{\mathrm e}^{4 x} c_1 +4 c_2 \,{\mathrm e}^{x}-x^{2}+x -3\right ) {\mathrm e}^{-3 x}}{4} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,3}]-2*D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Exp[-3*x]*(32-23*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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