88.6.5 problem 5

Internal problem ID [23987]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:49:20 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -(2*x + 3)*y(x)/(x**2 + 2*y(x)**2) + Derivative(y(x), x) cannot