77.25.1 problem 1

Internal problem ID [20606]
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 (B) at page 83
Problem number : 1
Date solved : Thursday, October 02, 2025 at 06:16:06 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

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

\[ y = c_1 +c_2 \,x^{3}+\frac {c_3}{x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {c_2 x^3}{3}-\frac {c_1}{x}+c_3 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 12

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

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