Internal problem ID [1501]
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 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y-{\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=exp(-2*x)*(2-17*x+3*x^2),y(x), singsol=all)
\[ y \relax (x ) = \left (x^{2}-5 x +1\right ) {\mathrm e}^{-2 x}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-3 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 39
DSolve[y'''[x]+3*y''[x]-y'[x]-3*y[x]==Exp[-2*x]*(2-17*x+3*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (e^x \left ((x-5) x+c_2 e^x+c_3 e^{3 x}+1\right )+c_1\right ) \\ \end{align*}