85.20.2 problem 3

Internal problem ID [22563]
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 52
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:51:35 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.532 (sec). Leaf size: 29

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

\[ y = \operatorname {RootOf}\left (x^{10} \textit {\_Z}^{40}+x^{10} \textit {\_Z}^{30}-c_1 \right )^{10} x^{2} \]

✓ Mathematica. Time used: 60.235 (sec). Leaf size: 1637

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

Too large to display

✗ Sympy

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

Timed Out