85.14.4 problem 3

Internal problem ID [22520]
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. C Exercises at page 41
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:45:26 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y^{\prime }&=\frac {3 x^{5}+3 x^{2} y^{2}}{2 x^{3} y-2 y^{3}} \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 33

ode:=diff(y(x),x) = (3*x^5+3*x^2*y(x)^2)/(2*x^3*y(x)-2*y(x)^3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{2}+\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} -6 \ln \left (x \right )+6 c_1 -\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )\right )\right ) x \right ) x \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 33

ode=D[y[x],x]==  ( 3*x^5+3*x^2*y[x]^2)/( 2*x^3*y[x] -2*y[x]^3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{3} \arctan \left (\frac {x^3}{y(x)^2}\right )+\frac {1}{6} \log \left (x^6+y(x)^4\right )=c_1,y(x)\right ] \]

✓ Sympy. Time used: 6.142 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x**5 - 3*x**2*y(x)**2)/(2*x**3*y(x) - 2*y(x)**3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + \frac {3 \log {\left (x \right )}}{2} + \frac {\log {\left (1 + \frac {y^{4}{\left (x \right )}}{x^{6}} \right )}}{4} - \frac {\operatorname {atan}{\left (\frac {y^{2}{\left (x \right )}}{x^{3}} \right )}}{2} = 0 \]