87.13.23 problem 27

Internal problem ID [23506]
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 : 27
Date solved : Thursday, October 02, 2025 at 09:42:33 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-12 x y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 32

ode:=2*x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)-12*x*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{x}+c_2 \,x^{\frac {7}{4}+\frac {\sqrt {65}}{4}}+c_3 \,x^{\frac {7}{4}-\frac {\sqrt {65}}{4}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 46

ode=2*x^3*D[y[x],{x,3}]+x^2*D[y[x],{x,2}]-12*x*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^{\frac {1}{4} \left (7+\sqrt {65}\right )}+c_1 x^{\frac {7}{4}-\frac {\sqrt {65}}{4}}+\frac {c_3}{x} \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**3*Derivative(y(x), (x, 3)) + x**2*Derivative(y(x), (x, 2)) - 12*x*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {C_{2}}{x^{- \frac {7}{4} + \frac {\sqrt {65}}{4}}} + C_{3} x^{\frac {7}{4} + \frac {\sqrt {65}}{4}} \]