34.14.9 problem 30

Internal problem ID [8066]
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 : Tuesday, September 30, 2025 at 05:15:03 PM
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: 0.258 (sec). Leaf size: 70

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]
 

\begin{align*} y(x)&\to \int _1^x\left (c_1 K[1]-c_2 \left (K[1]^3+1\right )\right )dK[1]+c_3\\ y(x)&\to \frac {1}{2} c_1 \left (x^2-1\right )+c_3\\ y(x)&\to c_3-\frac {1}{4} c_2 \left (x^4+4 x-5\right ) \end{align*}

✗ 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