Answer:
The slope of the curve at (3,1) is 3.
Step-by-step explanation:
The given differential equation is
[tex]y'(t)=t^2-6y^2[/tex]
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).
[tex]m=[y'(t)]_{(3,1)}[/tex]
[tex]m=[t^2-6y^2]_{(3,1)}[/tex]
Substitute t=3 and y=1 in the above equation, to find the slope.
[tex]m=(3)^2-6(1)^2[/tex]
[tex]m=9-6[/tex]
[tex]m=3[/tex]
Therefore the slope of the curve at (3,1) is 3.
