Consider the differential equation y prime left parenthesis t right parenthesisequalst squared minus 6 y squared and the solutio

Question

3 years ago

11

n curve that passes through the point (3,1). What is the slope of the curve at (3,1)?

1 answer:

White raven [17] · Answer 1 · 2022-05-07T12:27:21+03:00

Answer:

The slope of the curve at (3,1) is 3.

Step-by-step explanation:

The given differential equation is

$y'(t)=t^2-6y^2$

It is given that the solution curve is passing through the point (3,1).

The slope of a curve y(t) at a point (a,b) is the value of y'(t) at (a,b).

We need to find the slope of the curve at (3,1).

$m=[y'(t)]_{(3,1)}$

$m=[t^2-6y^2]_{(3,1)}$

Substitute t=3 and y=1 in the above equation, to find the slope.

$m=(3)^2-6(1)^2$

$m=9-6$

$m=3$

Therefore the slope of the curve at (3,1) is 3.