Consider the equation of the curve that passes through the point and has the given slope.

Question

Consider the equation of the curve that passes through the point and has the given slope.

(64,3), y’=2y/3x

1. write a differential equation dy/dx using the given slope.

dy/dx=

find the general solution of the differential equation. (Use c for any needed constant).

use the given point to find the particular solution of the differential equation.

Answer 1

dy/dx=2y/3x

dy/2y=dx/3x

ln 2y = ln 3x + C₁

e^2y = ce^3x

The initial condition makes c=e^-186