Internal problem ID [1527]
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 30.
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 }-4 y^{\prime }-4 y-{\mathrm e}^{-x} \left (\left (1-22 x \right ) \cos \left (2 x \right )-\left (6 x +1\right ) \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 54
dsolve(1*diff(y(x),x$3)+1*diff(y(x),x$2)-4*diff(y(x),x)-4*y(x)=exp(-x)*((1-22*x)*cos(2*x)-(1+6*x)*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = -\left (x -1\right ) {\mathrm e}^{-x} \cos \left (2 x \right )+\left (x +1\right ) {\mathrm e}^{-x} \sin \left (2 x \right )-\frac {5 \,{\mathrm e}^{-x}}{3}+{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 46
DSolve[1*y'''[x]+1*y''[x]-4*y'[x]-4*y[x]==Exp[-x]*((1-22*x)*Cos[2*x]-(1+6*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_3 e^{4 x}+e^x ((x+1) \sin (2 x)-(x-1) \cos (2 x)+c_2)+c_1\right ) \\ \end{align*}