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]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y={\mathrm e}^{-2 x} \left (3 x^{2}-17 x +2\right )} \]
✓ 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)
\[ y \left (x \right ) = \left (c_{3} {\mathrm e}^{2 x}+{\mathrm e}^{4 x} c_{1} +\left (x^{2}-5 x +1\right ) {\mathrm e}^{x}+c_{2} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 42
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]
\[ y(x)\to e^{-3 x} \left (e^x \left (x^2-5 x+1\right )+c_2 e^{2 x}+c_3 e^{4 x}+c_1\right ) \]