60.1.12 problem 12

Internal problem ID [10026]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 12
Date solved : Monday, January 27, 2025 at 06:18:41 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y^{2}-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 8

dsolve(diff(y(x),x) + y(x)^2 - 1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 44

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]\&\right ][-x+c_1] \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}