32.5.27 problem Exercise 11.29, page 97

Internal problem ID [5865]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.29, page 97
Date solved : Tuesday, March 04, 2025 at 11:49:27 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 11

ode:=diff(y(x),x) = 1+y(x)/x-y(x)^2/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \tanh \left (\ln \left (x \right )+c_{1} \right ) x \]

✓ Mathematica. Time used: 0.663 (sec). Leaf size: 43

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

\begin{align*} y(x)\to \frac {x \left (x^2-e^{2 c_1}\right )}{x^2+e^{2 c_1}} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}

✓ Sympy. Time used: 0.261 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1 - y(x)/x + y(x)**2/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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