Internal problem ID [1550]
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 53.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y-4 \,{\mathrm e}^{-x} \left (1-6 x \right )+2 x \cos \relax (x )-2 \sin \relax (x ) \left (x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(1*diff(y(x),x$3)+1*diff(y(x),x$2)-1*diff(y(x),x)-1*y(x)=4*exp(-x)*(1-6*x)-2*x*cos(x)+2*(1+x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \left ({\mathrm e}^{x} \cos \relax (x ) x +2 x^{3}-2 \sin \relax (x ) {\mathrm e}^{x}+2 x^{2}+2 x +1\right )+{\mathrm e}^{x} c_{1}+{\mathrm e}^{-x} c_{2}+c_{3} x \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 42
DSolve[1*y'''[x]+1*y''[x]-1*y'[x]-1*y[x]==4*Exp[-x]*(1-6*x)-2*x*Cos[x]+2*(1+x)*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sin (x)+x \cos (x)+e^{-x} (x (2 x (x+1)+2+c_2)+1+c_1)+c_3 e^x \\ \end{align*}