Internal problem ID [7593]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(diff(y(x),x) + y(x)^2 - 1=0,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (x +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.965 (sec). Leaf size: 22
DSolve[y'[x] + y[x]^2 - 1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tanh (x-c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}