76.23.7 problem 8

Internal problem ID [17727]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.1 (Definitions and examples). Problems at page 388
Problem number : 8
Date solved : Monday, March 31, 2025 at 04:26:05 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \end{align*}

✗ Maple

ode:=(-4+x)*diff(diff(diff(diff(y(x),x),x),x),x)+(1+x)*diff(diff(y(x),x),x)+tan(x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x-1)*D[y[x],{x,4}]+(x+1)*D[y[x],{x,2}]+Tan[x]*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 4)*Derivative(y(x), (x, 4)) + (x + 1)*Derivative(y(x), (x, 2)) + y(x)*tan(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve (x - 4)*Derivative(y(x), (x, 4)) + (x + 1)*Derivative(y(x), (x, 2)) + y(x)*tan(x)