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)