40.14.9 problem 30

Internal problem ID [6780]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 30
Date solved : Sunday, March 30, 2025 at 11:22:29 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 20

ode:=(2*x^3-1)*diff(diff(diff(y(x),x),x),x)-6*x^2*diff(diff(y(x),x),x)+6*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_3 \,x^{4}+c_2 \,x^{2}+4 c_3 x +c_1 \]

✓ Mathematica. Time used: 1.242 (sec). Leaf size: 31

ode=(2*x^3-1)*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+6*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}-c_2 x+c_3 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**2*Derivative(y(x), (x, 2)) + 6*x*Derivative(y(x), x) + (2*x**3 - 1)*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out