Internal problem ID [1562]
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 65.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y+{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 66
dsolve(diff(y(x),x$4)-0*diff(y(x),x$3)-2*diff(y(x),x$2)+0*diff(y(x),x)+y(x)=-exp(-x)*(4-9*x+3*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (x^{2}-2 x -1\right ) \left (-3 x^{2}+9 x -4\right ) {\mathrm e}^{-x}}{48 x^{2}-144 x +64}+{\mathrm e}^{x} c_{1}+{\mathrm e}^{-x} c_{2}+c_{3} {\mathrm e}^{x} x +c_{4} x \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 52
DSolve[y''''[x]-0*y'''[x]-2*y''[x]+0*y'[x]+1*y[x]==-Exp[-x]*(4-9*x+3*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{32} e^{-x} \left (2 x \left (-x^3+2 x^2+x-1+16 c_2\right )-3+32 c_1\right )+e^x (c_4 x+c_3) \\ \end{align*}