84.2.1 problem 1.6

Internal problem ID [22070]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.6
Date solved : Thursday, October 02, 2025 at 08:23:24 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

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