32.7.20 problem Exercise 20.21, page 220

Internal problem ID [5935]
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
Date solved : Monday, January 27, 2025 at 01:27:43 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y \left (x \right ) = \left ({\mathrm e}^{\frac {11 x}{6}} c_{1} +{\mathrm e}^{\frac {3 x}{2}} c_4 +c_{2} {\mathrm e}^{\frac {2 x}{3}}+c_3 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

DSolve[36*D[y[x],{x,4}]-37*D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_1 e^{11 x/6}+c_2 e^{2 x/3}+c_3 e^{3 x/2}+c_4\right ) \]