Internal problem ID [4070]
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 20.8, 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 }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-diff(y(x),x$3)-4*diff(y(x),x$2)+4*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-2 x}+c_{4} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 36
DSolve[y''''[x]-y'''[x]-4*y''[x]+4*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} c_1 e^{-2 x}+c_2 e^x+\frac {1}{2} c_3 e^{2 x}+c_4 \\ \end{align*}