60.4.33 problem 1489

Internal problem ID [11456]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1489
Date solved : Sunday, March 30, 2025 at 08:22:37 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve x**2*Derivative(y(x), (x, 3)) + (x + 1)*Derivative(y(x), (x, 2)) - y(x)