73.5.20 problem 6.7 (h)

Internal problem ID [15052]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (h)
Date solved : Thursday, March 13, 2025 at 05:33:06 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\begin{align*} y &= \frac {1}{\sqrt {c_{1} -2 x}\, x} \\ y &= -\frac {1}{\sqrt {c_{1} -2 x}\, x} \\ \end{align*}

✓ Mathematica. Time used: 0.429 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 0.662 (sec). Leaf size: 29

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

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