87.16.19 problem 19

Internal problem ID [23588]
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 119
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:43:15 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : solve: Cannot solve -x**2 - 3*x*Derivative(y(x), (x, 2)) + 4*y(x) + Derivative