Internal problem ID [4084]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.22, page 220.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\sqrt {5}\, x} \sin \relax (x )-c_{2} {\mathrm e}^{-\sqrt {5}\, x} \sin \relax (x )+c_{3} {\mathrm e}^{\sqrt {5}\, x} \cos \relax (x )+c_{4} {\mathrm e}^{-\sqrt {5}\, x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 49
DSolve[y''''[x]-8*y''[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\sqrt {5} x} \left (c_2 \cos (x)+c_4 \sin (x)+e^{2 \sqrt {5} x} (c_3 \cos (x)+c_1 \sin (x))\right ) \\ \end{align*}