89.32.1 problem 1

Internal problem ID [24961]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:45:03 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.229 (sec). Leaf size: 53

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

\begin{align*} y &= -\frac {4}{\sqrt {x}} \\ y &= \frac {4}{\sqrt {x}} \\ y &= \frac {c_1^{2} x +16}{2 c_1 x} \\ y &= \frac {c_1^{2}+16 x}{2 c_1 x} \\ \end{align*}

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 77

ode=x^3*D[y[x],x]^2+x^2*y[x]*D[y[x],x]+4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{2 x}\\ y(x)&\to \frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{2 x}\\ y(x)&\to -\frac {4}{\sqrt {x}}\\ y(x)&\to \frac {4}{\sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), x)**2 + x**2*y(x)*Derivative(y(x), x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*y(x) + sqrt(x**3*(x*y(x)**2 - 16)))