Решить дифференциальное уравнение y'+sqrt (x) * y=sqrt (x) * y^2.

y'+sqrt (x) * y=sqrt (x) * y^2

y'+y√ (x) = √ (x) * y²

y' = √ (x) * y² - y√ (x)

y' = √ (x) * (y² - y)

dx * (y' / (y^2 - y)) = (√ (x)) * dx

dx * (dy/dx / (y² - y)) = (√ (x)) dx

dy / (y² - y) = (√ (x)) dx

ʃdy / (y² - y) = ʃ√ (x) dx

ʃ√ (x) dx = (2*³√x²) / 3 + c1

ʃdy / (y² - y) = ʃdy/y (y - 1) = ln| (y - 1) / y|+c2

(2*³√x²) / 3 + c1 = ln| (y - 1) / y|+c2

e^ ((2*³√x²) / 3 + c1) - c2 = (y - 1) / y

e^ ((2*³√x²) / 3 + c1) - c2 = 1/y - 1

1/y = e^ ((2*³√x²) / 3 + c1) + 1-c2

y = 1: (e^ ((2*³√x²) / 3 + c1) - c2+1)