Internal problem ID [4589]
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 20.19, page 220.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$4)-2*diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} x +c_{3} {\mathrm e}^{\sqrt {2}\, x}+c_{4} {\mathrm e}^{-\sqrt {2}\, x} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 42
DSolve[y''''[x]-2*y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-\sqrt {2} x} \left (c_1 e^{2 \sqrt {2} x}+c_2\right )+c_4 x+c_3 \]