85.33.14 problem 14

Internal problem ID [22637]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 14
Date solved : Thursday, October 02, 2025 at 08:57:10 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (3-x^{2} y\right ) y^{\prime }&=x y^{2}+4 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 50

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

\begin{align*} y &= \frac {3+\sqrt {2 c_1 \,x^{2}-8 x^{3}+9}}{x^{2}} \\ y &= -\frac {-3+\sqrt {2 c_1 \,x^{2}-8 x^{3}+9}}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.433 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to \frac {3-\sqrt {-8 x^3+c_1 x^2+9}}{x^2}\\ y(x)&\to \frac {3+\sqrt {-8 x^3+c_1 x^2+9}}{x^2} \end{align*}

✗ Sympy

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

Timed Out