87.13.27 problem 31

Internal problem ID [23510]
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 : 31
Date solved : Thursday, October 02, 2025 at 09:42:35 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=x^6*diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)-12*x^4*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,x^{2}+c_3 \,x^{8}+c_4 \,x^{3}+c_5 x +c_6 x \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 49

ode=x^6*D[y[x],{x,6}]-12*x^4*D[y[x],{x,4}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x^8}{1680}+c_6 x^3+c_5 x^2+\left (c_4-\frac {c_1}{2}\right ) x+\frac {1}{2} c_1 x \log (x)+c_3 \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6*Derivative(y(x), (x, 6)) - 12*x**4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} x^{8} + C_{6} x \log {\left (x \right )} \]