8.1.4.22 Geometric and physical applications

Problem: Find the integral curve of the equation \( y y^{\prime \prime}+ \) \( +\left(y^{\prime}\right)^{2}-1=0 \) passing through the point \( M_{0}(0,1) \), and tangent at this point to the line \( x+y=1 \). clip2net.com