(1 + e^x) * y * y' = e^x
(1 + e^x) * y * dy/dx = e^x
y dy = e^x/(1 + e^x) dx
int y dy = int e^x/(1 + e^x) dx
1/2 * y^2 = int d(e^x)/(1 + e^x)
1/2 * y^2 = int d(1 + e^x)/(1 + e^x)
1/2 * y^2 = ln (1 + e^x) + C
y^2 = 2 * ln (1 + e^x) + C
Бесплатно.