Ordinary differential equations

[ra_forever8]

Consider the first order differential equation
dy/dt = f(t,y)= -16t^3y^2, with the inital condition y(0)=1.
Estimate the lipschitz derivative for the differential equation by substituting the exact solution into ∂f/∂y.

=I found the exact solution by using the separable of variable and doing integration
which is y(t)= (4t^4 +1)^-1
And also i found the ∂f/∂y = -32yt^3
The question ask about by substituting the exact solution into ∂f/∂y to estimate the lipschitz derivative. I don't know how to substitute.
Does anyone knows about lipschitz derivative?

Help me Please.

 

[Ray Vickson]

Consider the first order differential equation
dy/dt = f(t,y)= -16t^3y^2, with the inital condition y(0)=1.
Estimate the lipschitz derivative for the differential equation by substituting the exact solution into ∂f/∂y.

=I found the exact solution by using the separable of variable and doing integration
which is y(t)= (4t^4 +1)^-1
And also i found the ∂f/∂y = -32yt^3
The question ask about by substituting the exact solution into ∂f/∂y to estimate the lipschitz derivative. I don't know how to substitute.
Does anyone knows about lipschitz derivative?

Help me Please.

1) Read your textbook; or
2) Google 'lipschitz derivative'.

 

[ra_forever8]

I can not find it. So, i was asking for help.