80.8.11 problem 14

Internal problem ID [18519]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 14
Date solved : Monday, March 31, 2025 at 05:41:06 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime }&=17 x^{6} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

ode:=x^4*diff(diff(diff(diff(y(x),x),x),x),x)+x^3*diff(diff(diff(y(x),x),x),x)-20*x^2*diff(diff(y(x),x),x)+20*x*diff(y(x),x) = 17*x^6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {612 \ln \left (x \right ) x^{9}+\left (1296 c_3 -323\right ) x^{9}+3888 c_1 \,x^{5}+7776 c_4 \,x^{3}-2592 c_2}{7776 x^{3}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 49

ode=x^4*D[y[x],{x,4}]+x^3*D[y[x],{x,3}]-20*x^2*D[y[x],{x,2}]+20*x*D[y[x],x]==17*x^6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {17}{216} x^6 \log (x)+\left (-\frac {323}{7776}+\frac {c_3}{6}\right ) x^6-\frac {c_1}{3 x^3}+\frac {c_2 x^2}{2}+c_4 \]

✓ Sympy. Time used: 0.373 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-17*x**6 + x**4*Derivative(y(x), (x, 4)) + x**3*Derivative(y(x), (x, 3)) - 20*x**2*Derivative(y(x), (x, 2)) + 20*x*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {C_{2}}{x^{3}} + C_{3} x^{2} + C_{4} x^{6} + \frac {17 x^{6} \log {\left (x \right )}}{216} \]