1.7.8 problem 8

Internal problem ID [186]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 03:48:40 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \frac {3 x}{3 c_1 \,x^{3}+1} \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {3 x}{1+3 c_1 x^3}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {3 x}{C_{1} x^{3} + 1} \]