Internal problem ID [4072]
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 20.10, 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 }-a^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 38
dsolve(diff(y(x),x$4)-a^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\sqrt {a}\, x}+c_{2} {\mathrm e}^{-\sqrt {a}\, x}+c_{3} \sin \left (\sqrt {a}\, x \right )+c_{4} \cos \left (\sqrt {a}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 53
DSolve[y''''[x]-a^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 e^{-\sqrt {a} x}+c_4 e^{\sqrt {a} x}+c_1 \cos \left (\sqrt {a} x\right )+c_3 \sin \left (\sqrt {a} x\right ) \\ \end{align*}