30.5.36 problem 47 (b)

Internal problem ID [7535]
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 : 47 (b)
Date solved : Tuesday, September 30, 2025 at 04:44:55 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} y^{\prime }&=x^{3} \left (y-x \right )^{2}+\frac {y}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \frac {x \left (x^{5}+5 c_1 -5\right )}{x^{5}+5 c_1} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to \frac {x \left (x^5-5+5 c_1\right )}{x^5+5 c_1}\\ y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {x \left (C_{1} + x^{5} - 6\right )}{C_{1} + x^{5} - 1} \]