89.9.8 problem 8

Internal problem ID [24488]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 72
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:42:25 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} y^{2}+\left (3 y x +y^{2}-1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

ode:=y(x)^2+(3*x*y(x)+y(x)^2-1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {\frac {\left (y^{2}-1\right )^{2}}{4}-c_1}{y^{3}} = 0 \]

✓ Mathematica. Time used: 60.124 (sec). Leaf size: 1751

ode=y[x]^2+( 3*x*y[x] +y[x]^2-1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 33.320 (sec). Leaf size: 4009

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x*y(x) + y(x)**2 - 1)*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]