Sales and pricing

[mathcanada]

Suppose that a chain of auto service stations, has found that the relationship between its price p for an oil change and its monthly sales volume y, in thousands of dollars, is dy/dp=-1/2(y/(p+5))

Solve this differential equation if y=18 when p=$20.

I'm having alot of problem with this question if anyone can help out it would be greatly appreciated. Thanks.

 

[Unco]

I think you mean

dy/dp=(-1/2)(y/(p+5))

In which case* seperate variables. To begin, divide both sides by y. Then you can integrate both sides wrt p.

You'll have to let us know where you get stuck from there.

* If it is dy/dp=-1/[2(y/(p+5)], then multiply by y instead.