85.17.1 problem 2

Internal problem ID [22546]
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 48
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:49:38 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.180 (sec). Leaf size: 35

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

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{9} c_1 +3 \textit {\_Z}^{5} c_1 -x \sqrt {\frac {x}{c_1}}\right )^{4}+3}{x} \]

✓ Mathematica. Time used: 6.503 (sec). Leaf size: 856

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.360 (sec). Leaf size: 26

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

\[ - \log {\left (x \right )} + \frac {2 \log {\left (x y{\left (x \right )} \right )}}{3} + \frac {5 \log {\left (x y{\left (x \right )} - 3 \right )}}{6} = C_{1} \]