71.10.7 problem 7

Internal problem ID [14431]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 7
Date solved : Monday, March 31, 2025 at 12:27:01 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=36*diff(diff(diff(diff(y(x),x),x),x),x)-12*diff(diff(diff(y(x),x),x),x)-11*diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{3}} \left (\left (c_2 x +c_1 \right ) {\mathrm e}^{\frac {5 x}{6}}+c_4 x +c_3 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 41

ode=36*D[y[x],{x,4}]-12*D[y[x],{x,3}]-11*D[y[x],{x,2}]+2*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x/3} \left (c_3 e^{5 x/6}+x \left (c_4 e^{5 x/6}+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.219 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 2*Derivative(y(x), x) - 11*Derivative(y(x), (x, 2)) - 12*Derivative(y(x), (x, 3)) + 36*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- \frac {x}{3}} + \left (C_{3} + C_{4} x\right ) e^{\frac {x}{2}} \]