83.24.3 problem 3

Internal problem ID [19238]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (A) at page 81
Problem number : 3
Date solved : Thursday, March 13, 2025 at 02:04:31 PM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {x^{1+\sqrt {2}} c_{2} +x^{1-\sqrt {2}} c_3 +c_{1}}{x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 34

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

\[ y(x)\to c_2 x^{-\sqrt {2}}+c_1 x^{\sqrt {2}}+\frac {c_3}{x} \]

✓ Sympy. Time used: 0.086 (sec). Leaf size: 22

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

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