82.8.15 problem 36-16

Internal problem ID [21886]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-16
Date solved : Thursday, October 02, 2025 at 08:05:44 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.202 (sec). Leaf size: 51

ode:=x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+9*x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -2 x^{{3}/{2}} \\ y &= 2 x^{{3}/{2}} \\ y &= \frac {c_1^{2} x^{3}+4}{2 c_1} \\ y &= \frac {4 x^{3}+c_1^{2}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 79

ode=x*D[y[x],x]^2-3*y[x]*D[y[x],x]+9*x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right )\\ y(x)&\to \frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right )\\ y(x)&\to -2 x^{3/2}\\ y(x)&\to 2 x^{3/2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2 + x*Derivative(y(x), x)**2 - 3*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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