Internal problem ID [4592]
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]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y=0} \]
✓ 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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\sqrt {5}\, x} \sin \left (x \right )-c_{2} {\mathrm e}^{-\sqrt {5}\, x} \sin \left (x \right )+c_{3} {\mathrm e}^{\sqrt {5}\, x} \cos \left (x \right )+c_{4} {\mathrm e}^{-\sqrt {5}\, x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 142
DSolve[y''''[x]-8*y''[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )} \left (\left (c_3 e^{2 \sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )}+c_2\right ) \cos \left (\sqrt {6} x \sin \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )\right )+\sin \left (\sqrt {6} x \sin \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )\right ) \left (c_1 e^{2 \sqrt {6} x \cos \left (\frac {1}{2} \arctan \left (\frac {\sqrt {5}}{2}\right )\right )}+c_4\right )\right ) \]