87.13.22 problem 26

Internal problem ID [23505]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 100
Problem number : 26
Date solved : Thursday, October 02, 2025 at 09:42:33 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 2 x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=2*x^4*diff(diff(diff(diff(y(x),x),x),x),x)+3*x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)-8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}+c_2 x +c_3 \,x^{\frac {3}{4}+\frac {\sqrt {41}}{4}}+c_4 \,x^{\frac {3}{4}-\frac {\sqrt {41}}{4}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 50

ode=2*x^4*D[y[x],{x,4}]+3*x^3*D[y[x],{x,3}]-4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]-8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^{\frac {1}{4} \left (3+\sqrt {41}\right )}+c_1 x^{\frac {3}{4}-\frac {\sqrt {41}}{4}}+c_4 x^2+c_3 x \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**4*Derivative(y(x), (x, 4)) + 3*x**3*Derivative(y(x), (x, 3)) - 4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{2} + \frac {C_{3}}{x^{- \frac {3}{4} + \frac {\sqrt {41}}{4}}} + C_{4} x^{\frac {3}{4} + \frac {\sqrt {41}}{4}} \]