87.8.8 problem 8

Internal problem ID [23362]
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 65
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:40:33 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \end{align*}

✗ Maple

ode:=2*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-4*diff(y(x),x)+x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=2*D[y[x],{x,3}]+3*D[y[x],{x,2}]-4*D[y[x],{x,1}]+x*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*y(x) - 4*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x*y(x)/4 + Derivative(y(x), x) - 3*Derivative(y(x), (x, 2))/4 -