# Ordinary differential equations

1. Nov 28, 2013

### 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?

2. Nov 28, 2013