87.13.20 problem 24

Internal problem ID [23503]
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 : 24
Date solved : Thursday, October 02, 2025 at 09:42:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = c_1 \,x^{{4}/{3}}+c_2 x +c_3 x \ln \left (x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to x \left (c_1 \sqrt [3]{x}+c_3 \log (x)+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.136 (sec). Leaf size: 19

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

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