87.10.6 problem 7

Internal problem ID [23407]
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 79
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:41:11 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0 \end{align*}

With initial conditions

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

✗ Maple

ode:=(x^3-1)*diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+4*x*y(x) = 0; 
ic:=[y(-1) = 0, D(y)(-1) = 2, (D@@2)(y)(-1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^3-1)*D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*x*y[x]==0; 
ic={y[-1]==0,Derivative[1][y][-1] ==2,Derivative[2][y][-1] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*y(x) + (x**3 - 1)*Derivative(y(x), (x, 3)) - 3*Derivative(y(x), (x, 2)),0) 
ics = {y(-1): 0, Subs(Derivative(y(x), x), x, -1): 2, Subs(Derivative(y(x), (x, 2)), x, -1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve 4*x*y(x) + (x**3 - 1)*Derivative(y(x), (x, 3)) - 3*Derivat