Internal problem ID [2226]
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 33.
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 }-13 y^{\prime \prime }+36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)-13*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x}+c_{4} {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]-13*y''[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (c_2 e^x+e^{5 x} \left (c_4 e^x+c_3\right )+c_1\right ) \\ \end{align*}