Internal problem ID [4013]
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]
Solve \begin {gather*} \boxed {y^{\prime }-1-\frac {y}{x}+\frac {y^{2}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve(diff(y(x),x)=1+y(x)/x-y(x)^2/x^2,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.469 (sec). Leaf size: 38
DSolve[y'[x]==1+y[x]/x-y[x]^2/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\frac {2 x^3}{x^2+e^{2 c_1}} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}