Internal problem ID [1513]
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 16.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime \prime }-11 y^{\prime \prime }-9 y^{\prime }-2 y+{\mathrm e}^{x} \left (1-6 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
dsolve(4*diff(y(x),x$4)-11*diff(y(x),x$2)-9*diff(y(x),x)-2*y(x)=-exp(x)*(1-6*x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (x -1\right ) \left (6 x \,{\mathrm e}^{x}-{\mathrm e}^{x}\right )}{3 \left (6 x -1\right )}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-\frac {x}{2}}+c_{4} {\mathrm e}^{-\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 47
DSolve[4*y''''[x]-11*y''[x]-9*y'[x]-2*y[x]==-Exp[x]*(1-6*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} e^x (x-1)+e^{-x/2} (c_2 x+c_1)+c_3 e^{-x}+c_4 e^{2 x} \\ \end{align*}