Internal problem ID [1512]
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 15.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 94
dsolve(diff(y(x),x$4)+8*diff(y(x),x$3)+24*diff(y(x),x$2)+32*diff(y(x),x)=-16*exp(-2*x)*(1+x+x^2-x^3),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{3} {\mathrm e}^{-2 x} \left (-2 \sin \left (2 x \right )-2 \cos \left (2 x \right )\right )}{8}+2 c_{2} \left (\frac {\left (-2 \cos \relax (x )+2 \sin \relax (x )\right ) {\mathrm e}^{-2 x} \cos \relax (x )}{8}-\frac {{\mathrm e}^{-2 x}}{8}\right )+\frac {c_{2} {\mathrm e}^{-2 x}}{2}-\frac {{\mathrm e}^{-4 x} c_{1}}{4}-{\mathrm e}^{-2 x} x^{3}+{\mathrm e}^{-2 x} x^{2}+{\mathrm e}^{-2 x} x +{\mathrm e}^{-2 x}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.719 (sec). Leaf size: 62
DSolve[y''''[x]+8*y'''[x]+24*y''[x]+32*y'[x]==-16*Exp[-2*x]*(1+x+x^2-x^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-2 x} \left (4 x \left (-x^2+x+1\right )-c_3 e^{-2 x}-(c_1+c_2) \cos (2 x)+(c_2-c_1) \sin (2 x)+4\right )+c_4 \\ \end{align*}