77.1.103 problem Example 1 (page 195)

Internal problem ID [17914]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : Example 1 (page 195)
Date solved : Thursday, March 13, 2025 at 11:10:29 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 16

ode:=2*x^3*diff(diff(diff(y(x),x),x),x)-6*x^2*diff(diff(y(x),x),x)+12*x*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 19

ode=2*x^3*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+12*x*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x (x (c_3 x+c_2)+c_1) \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**3*Derivative(y(x), (x, 3)) - 6*x**2*Derivative(y(x), (x, 2)) + 12*x*Derivative(y(x), x) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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