Internal problem ID [1534]
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 37.
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 }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y-{\mathrm e}^{x} \left (8 \cos \relax (x )+16 \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 45
dsolve(1*diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x$2)-8*diff(y(x),x)-8*y(x)=exp(x)*(8*cos(x)+16*sin(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\cos \relax (x ) {\mathrm e}^{x}}{10}-\frac {7 \sin \relax (x ) {\mathrm e}^{x}}{10}+{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \cos \relax (x ) {\mathrm e}^{-x}+c_{4} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 53
DSolve[1*y''''[x]+2*y'''[x]-2*y''[x]-8*y'[x]-8*y[x]==Exp[x]*(8*Cos[x]+16*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}-\frac {1}{10} e^x (7 \sin (x)+\cos (x))+e^{-x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}