30.6.7 problem 8

Internal problem ID [7542]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 04:45:09 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {1}{\left (-2 x +c_1 \right ) x^{2}} \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -\frac {1}{x^2 (2 x-c_1)}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {1}{x^{2} \left (C_{1} - 2 x\right )} \]