30.5.21 problem 21

Internal problem ID [7520]
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 : 21
Date solved : Tuesday, September 30, 2025 at 04:41:48 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to -\frac {2}{x^3-2 c_1 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 10

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

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