73.9.9 problem 14.1 (i)

Internal problem ID [15191]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (i)
Date solved : Thursday, March 13, 2025 at 05:49:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 94

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+6*diff(diff(y(x),x),x)+3*diff(y(x),x)-83*y(x)-25 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {25}{83}+c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =1\right ) x}+c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =2\right ) x}+c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =4\right ) x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 117

ode=D[y[x],{x,4}]+6*D[y[x],{x,2}]+3*D[y[x],x]-83*y[x]-25==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,1\right ]\right )-\frac {25}{83} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-83*y(x) + 3*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)) - 25,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -83*y(x)/3 + Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4))/3 - 25/3 cannot be solved by the factorable group method