Internal problem ID [4083]
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 20.21, page 220.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(36*diff(y(x),x$4)-37*diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{-\frac {x}{3}}+c_{4} {\mathrm e}^{\frac {5 x}{6}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 44
DSolve[36*y''''[x]-37*y''[x]+4*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (c_1 e^{11 x/6}+c_2 e^{2 x/3}+c_3 e^{3 x/2}+c_4\right ) \\ \end{align*}