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 : Monday, January 27, 2025 at 01:21:37 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==1+y[x]/x-y[x]^2/x^2,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*}