solve the following DE

Question

∫₀^x y(t)dt= -x/y(x)

*difinite integral from 0 to x

Answer 1

∫₀^x y(t)dt= -x/y(x)

d/dx [ ∫₀^x y(t)dt ] = - d/dx [x/y(x)]

y(x) = - d/dx [x/y(x)]

y = - 1/y + [ x/y²] [ d y / d x]

d y / d x - (1/ x) y = (1/ x) y³ BERNOULLI