The rate of change of y with respect to x is one-half times the value of y. Find an equation for y, given that y = -7 when x = 0.

You get: (see attachment)

Question

The rate of change of y with respect to x is one-half times the value of y. Find an equation for y, given that y = -7 when x = 0.

You get: (see attachment)

anonymous · Answer

attachment

blockcolder · Answer

Thus, the differential equation can be written as:
$$\frac{dy}{dx}=\frac{y}{2}; y(0)=-7$$
Can you solve this?

anonymous · Answer

basically we have to find an equation. what would be the first step?

blockcolder · Answer

Examine the form of the differential equation. Since there are only y's and no x's, separation of variables seems to be the best solution.

anonymous · Answer

so i multiply dx and dy on both sides, right?

blockcolder · Answer

No, you multiply both sides by dx/y. Tell me what you get after this.

anonymous · Answer

is that dx divided by y or dx and y?

blockcolder · Answer

dx divided by y.

anonymous · Answer

lol, honestly im stuck. i'm still trying to learn how to deal with derivative aigns and stuff.

anonymous · Answer

*signs

blockcolder · Answer

It's ok. I'll help you.
$$\frac{dy}{dx}=\frac{y}{2}\
\frac{dy}{y}=\frac{dx}{2}\
\int\frac{dy}{y}=\int\frac{dx}{2}$$
Hopefully, you'll know what to do from here. :D

anonymous · Answer

oh I see....the dx on the left and the y on the right got eliminated  since your multiplying them. I thought about that, I just didn't know what to put over the y  after the dx from dx/y got eliminated and so on.

blockcolder · Answer

Do you have an answer now? :D

anonymous · Answer

is it A?

blockcolder · Answer

It's not A because that is not an equation in y.

anonymous · Answer

don't tell me the answer.

anonymous · Answer

is it C?

blockcolder · Answer

It's not C.

anonymous · Answer

I got it wrong. It was B. anyway, thanks.