Internal problem ID [4521]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y^{\prime }-\frac {y}{x}+\frac {y^{2}}{x^{2}}=1} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.539 (sec). Leaf size: 43
DSolve[y'[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*}