Question

Resolva a Equação diferencial
dy/dx = 1/x

a) e^y = k
b) e^y = x.k
c) y = lnx
d) x= lnx + c
e) y = lny + c

Answer 1

Olá


$\displaystyle \mathsf{ \frac{dy}{dx}= \frac{1}{x} }\\\\\\\mathsf{dy= \frac{dx}{x} }\\\\\\\text{Integrando dos dois lados}\\\\\\\mathsf{\int dy= \int \frac{dx}{x} }\\\\\\\boxed{\mathsf{y=\ell n|x|+C}}$