Internal problem ID [1499]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {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 )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 35
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)
\[ y \relax (x ) = -\frac {\left (x^{2}-x +3\right ) {\mathrm e}^{-3 x}}{4}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 44
DSolve[y'''[x]-2*y''[x]-5*y'[x]+6*y[x]==Exp[-3*x]*(32-23*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} e^{-3 x} ((x-1) x+3)+c_1 e^{-2 x}+c_2 e^x+c_3 e^{3 x} \\ \end{align*}