30.5.35 problem 46

Internal problem ID [7534]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 46
Date solved : Tuesday, September 30, 2025 at 04:44:50 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.134 (sec). Leaf size: 1085

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

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

✓ Mathematica. Time used: 60.123 (sec). Leaf size: 1893

ode=D[y[x],x]==3*x*y[x]/( 2*x^2 - y[x]^2 ); 
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(-3*x*y(x)/(2*x**2 - y(x)**2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out