84.17.2 problem 10.1 (b)

Internal problem ID [22194]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Solved problems. Page 54
Problem number : 10.1 (b)
Date solved : Thursday, October 02, 2025 at 08:33:58 PM
CAS classification : [[_3rd_order, _exact, _nonlinear]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2 - y(x)*Derivative(y(x), (x, 3)) - y(x))/x cannot be solved by the factorable group method