Internal problem ID [4034]
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]
Solve \begin {gather*} \boxed {y^{\prime } x -y^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve(x*diff(y(x),x)-y(x)^2+1=0,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (c_{1}+\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.686 (sec). Leaf size: 33
DSolve[x*y'[x]-y[x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {2}{1+e^{2 c_1} x^2} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}