Question

PLEASE HELP I HAVE A TEST IN AN HOUR. Considering the differential equation dy/dx=2x-y, the solution curve that passes through the point (0,1) has a local minimum at x=ln(3/2). What is the y-coordinate of this local minimum?

Answer 1

y' + y = 2x ; whats the homogenous solution? whats the particular solution?

Answer 2

a local minimum is also known as y'=0, sooo, 0 = 2x-y should let us solve for that part right? or do we need to work it from the solution of the diffy q?

Answer 3

but if you did use 0=2x-y, and substituted the ln(3/2) as x, then you would get y=2(ln(3/2)) which doesn't make sense to me... right?

Answer 4

why doesnt it make sense to you? what is the value of y' (what is the slope of the line) at a minimum (or maximum)?

Answer 5

Asking a similar question: Given the function f(x), how would you locate the critical value or values? Hint: one of the two types of critical values is an x value at which the derivative equals zero (that is, the slope of the tangent line to the graph is zero).

You are given a formula for the slope. Why not set it equal to zero and solve the resulting equation for y? How would y ou then calculate y?

Answer 6

we can chk this by solving the diffy Q if need be :) whats your process?

Answer 7

Suggestion, Anna: Identify the type of d. e. you have here: separable or first order linear.