85.34.9 problem 9

Internal problem ID [22717]
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. B Exercises at page 67
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:11:48 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.054 (sec). Leaf size: 34

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

\[ y = \frac {{\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{2 \textit {\_Z}}-4 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+4 c_1 \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \]

✗ Mathematica

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

Not solved

✓ Sympy. Time used: 0.836 (sec). Leaf size: 27

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

\[ - \frac {x y{\left (x \right )}}{4} - \log {\left (x \right )} + \frac {\log {\left (x y{\left (x \right )} \right )}}{2} + \frac {1}{4 x y{\left (x \right )}} = C_{1} \]