Internal problem ID [1560]
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 63.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)+1*diff(y(x),x)-0*y(x)=-2*exp(-x)*(7-18*x+6*x^2),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \left (x^{4}-2 x^{3}+x^{2}-x c_{1}+2 x -c_{1}-c_{2}+2\right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 42
DSolve[y'''[x]+2*y''[x]+1*y'[x]-0*y[x]==-2*Exp[-x]*(7-18*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (x \left (x (x-1)^2+2-c_2\right )+c_3 e^x+2-c_1-c_2\right ) \\ \end{align*}