87.13.25 problem 29

Internal problem ID [23508]
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 : 29
Date solved : Thursday, October 02, 2025 at 09:42:34 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y&=0 \end{align*}

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

ode:=7*x^4*diff(diff(diff(diff(y(x),x),x),x),x)-2*x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-6*x*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{2}+c_2 x +c_3 \,x^{\frac {23}{14}+\frac {\sqrt {445}}{14}}+c_4 \,x^{\frac {23}{14}-\frac {\sqrt {445}}{14}} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 50

ode=7*x^4*D[y[x],{x,4}]-2*x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^{\frac {1}{14} \left (23+\sqrt {445}\right )}+c_1 x^{\frac {1}{14} \left (23-\sqrt {445}\right )}+c_4 x^2+c_3 x \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*x**4*Derivative(y(x), (x, 4)) - 2*x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) - 6*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{2} + C_{3} x^{\frac {23}{14} - \frac {\sqrt {445}}{14}} + C_{4} x^{\frac {\sqrt {445}}{14} + \frac {23}{14}} \]