What is a solution to the differential equation $dy/dx=ky$ ?

Question

33585 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-04T14:04:39

$abs y = C e^(kx)$

Assiuming k is just some constant, this is immediately separable

$1/y y' = k$

And
$int (1/y y' = k) dx$

$implies int 1/y \ dy = k int dx$

$implies ln abs y = k x + C$

$abs y = e^(k x + C) = C e^(kx)$

What is a solution to the differential equation dy/dx=kydy/dx=ky?