Question

How do you use the differential equation `dy/dx=-48/(3x+5)^3` to find the equation of the function given point (-1,3)?

Answer 1

`y=8/(3x+5)^2+1`

Explanation:

Either by sight or by substituting `u=3x+5` youfind that `y=8/(3x+5)^2+c`
To make this curve pass through the point `(-1,3)`, insert the co-ordinates and solve for `c`:
`3=8/(3(-1)+5)^2+c`
So `c=1`.