Internal problem ID [1563]
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 66.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y-{\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \relax (x )+\left (8-9 x \right ) \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=exp(-2*x)*((23-2*x)*cos(x)+(8-9*x)*sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\cos \relax (x ) {\mathrm e}^{-2 x} x}{2}+{\mathrm e}^{-2 x} \cos \relax (x )-2 \sin \relax (x ) {\mathrm e}^{-2 x} x +\frac {3 \,{\mathrm e}^{-2 x} \sin \relax (x )}{2}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 48
DSolve[y'''[x]+2*y''[x]-y'[x]-2*y[x]==Exp[-2*x]*((23-2*x)*Cos[x]+(8-9*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-2 x} \left ((3-4 x) \sin (x)+(x+2) \cos (x)+2 \left (c_2 e^x+c_3 e^{3 x}+c_1\right )\right ) \\ \end{align*}