1.12 problem 12

Internal problem ID [8349]

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]

\[ \boxed {y^{\prime }+y^{2}=1} \]

✓ 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)
 

\[ y \left (x \right ) = \tanh \left (x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.638 (sec). Leaf size: 44

DSolve[y'[x] + y[x]^2 - 1==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\begin{align*} y(x)\to \frac {e^{2 x}-e^{2 c_1}}{e^{2 x}+e^{2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}