Internal problem ID [4542]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.21, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-y^{2}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(x*diff(y(x),x)-y(x)^2+1=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (\ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 43
DSolve[x*y'[x]-y[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-e^{2 c_1} x^2}{1+e^{2 c_1} x^2} y(x)\to -1 y(x)\to 1 \end{align*}