15.16.14 problem 14

Internal problem ID [3234]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 14
Date solved : Sunday, March 30, 2025 at 01:23:25 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y&=\frac {4}{x^{2}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 41

ode:=3*x^3*diff(diff(diff(y(x),x),x),x)+4*x^2*diff(diff(y(x),x),x)-10*x*diff(y(x),x)+10*y(x) = 4/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {9 c_2 \,x^{\frac {7}{3}-\frac {\sqrt {31}}{3}}+9 c_3 \,x^{\frac {7}{3}+\frac {\sqrt {31}}{3}}+9 c_1 \,x^{3}-2}{9 x^{2}} \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 51

ode=3*x^3*D[y[x],{x,3}]+4*x^2*D[y[x],{x,2}]-10*x*D[y[x],x]+10*y[x]==4/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x^{\frac {1}{3} \left (1+\sqrt {31}\right )}+c_1 x^{\frac {1}{3}-\frac {\sqrt {31}}{3}}-\frac {2}{9 x^2}+c_3 x \]

✓ Sympy. Time used: 0.445 (sec). Leaf size: 65

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**3*Derivative(y(x), (x, 3)) + 4*x**2*Derivative(y(x), (x, 2)) - 10*x*Derivative(y(x), x) + 10*y(x) - 4/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + \frac {C_{2} \sqrt [3]{x}}{x^{\frac {\sqrt {31}}{3}}} + C_{3} \sqrt [3]{x} x^{\frac {\sqrt {31}}{3}} - \frac {2 x^{- \frac {1}{3} + \frac {\sqrt {31}}{3}}}{9 x^{\frac {5}{3}} x^{\frac {\sqrt {31}}{3}}} \]