Internal problem ID [2225]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 32.
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 }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)-diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+{\mathrm e}^{-x} c_{2}+c_{3} {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 34
DSolve[y''''[x]-2*y'''[x]-y''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (-e^{-x}\right )+c_2 e^x+\frac {1}{2} c_3 e^{2 x}+c_4 \\ \end{align*}