Internal problem ID [1526]
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 29.
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 (16+10 x \right ) \cos \relax (x )+\left (30-10 x \right ) \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(0*diff(y(x),x$4)+1*diff(y(x),x$3)-1*diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(-x)*((16+10*x)*cos(x)+(30-10*x)*sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \cos \relax (x ) {\mathrm e}^{-x} x +{\mathrm e}^{-x} \cos \relax (x )-\sin \relax (x ) {\mathrm e}^{-x} x +2 \,{\mathrm e}^{-x} \sin \relax (x )+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 47
DSolve[0*y''''[x]+1*y'''[x]-1*y''[x]-4*y'[x]+4*y[x]==Exp[-x]*((16+10*x)*Cos[x]+(30-10*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{3 x} \left (c_3 e^x+c_2\right )+e^x ((x+1) \cos (x)-(x-2) \sin (x))+c_1\right ) \\ \end{align*}