Internal problem ID [1510]
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 13.
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 }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }-7 y^{\prime }+6 y+3 \,{\mathrm e}^{-x} \left (-8 x^{2}+8 x +12\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 62
dsolve(diff(y(x),x$4)+3*diff(y(x),x$3)-3*diff(y(x),x$2)-7*diff(y(x),x)+6*y(x)=-3*exp(-x)*(12+8*x-8*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x^{2}-2 x +1\right ) \left (24 x^{2}-24 x -36\right ) {\mathrm e}^{-x}}{8 x^{2}-8 x -12}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-3 x}+c_{3} {\mathrm e}^{-2 x}+c_{4} x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 44
DSolve[y''''[x]+3*y'''[x]-3*y''[x]-7*y'[x]+6*y[x]==-3*Exp[-x]*(12+8*x-8*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (e^x \left (3 e^x (x-1)^2+e^{3 x} (c_4 x+c_3)+c_2\right )+c_1\right ) \\ \end{align*}