dy/dx=y,
solve for y as a f(x)

Question

dy/dx=y,
solve for y as a f(x)

anonymous · Answer

is it IMPLICIT DIFFERENTIATION!

anonymous · Answer

ok

anonymous · Answer

so is it?

anonymous · Answer

no, It is an ODE

anonymous · Answer

okay

anonymous · Answer

The derivative of a function Y with respect to x is Y itself, I don't know what Y would have to be in that case.

ribhu · Answer

no derivative of y with respect to x is dy/dx

anonymous · Answer

@ribhu  is right

ribhu · Answer

see in your problem take all the y terms on one side and all the x terms on one side. since your differential equation is separable. @VeronicaEsc

ribhu · Answer

$$dy/y = dx$$
would be obtained after rearrangement.

anonymous · Answer

how can you separate dy/dx, I thought that was just an operator

ribhu · Answer

in differential equations of this kind you can do it.

ribhu · Answer

variable separable form differential equation. @VeronicaEsc .

anonymous · Answer

Okay, so would I proceed to integrate both sides now

ribhu · Answer

yeah that would be the solution along with the constant of integration.

anonymous · Answer

How does one integrate dy/y

ribhu · Answer

it is lny

anonymous · Answer

why?

ribhu · Answer

its the basic formula or you can know from by parts.

anonymous · Answer

Ln means Log of base e correct?

ribhu · Answer

d(lny)=1/y
now integrating both the sides so we get 
lny = integration dy/y.

ribhu · Answer

yeah correct.

ribhu · Answer

was i of any help to you?

anonymous · Answer

Yes, I know what to do from here

anonymous · Answer

Thank you, very much!

ribhu · Answer

$$dy/y = dx $$
$$\int\limits_{}dy/y{} = \int\limits_{}^{}dx$$

ribhu · Answer

$$\ln y = x + c$$
@VeronicaEsc did u get the answer?

anonymous · Answer

Yes

ribhu · Answer

so liked the way i explained it to u