I don't know what equations they want me to found here:
Let $\phi(t,t_0,x_0,(a,b))$ be the solution to the IVP
$$\begin{cases}\dot{x}=2t(ax-bx^2) \\x(t_0)=x_0\end{cases}$$
Prove that the derivatives $\partial\phi_{x_0}(t,0,1,(1,0))$, $\ \partial\phi_{a}(t,0,1,(1,0))$, $\ \partial\phi_{b}(t,0,1,(1,0))$ are the same that the ones we obtain using the differentiable dependence theorem on initial conditions and parameters.
I know how to solve this system and how to find $\partial\phi_{x_0}(t,0,1,(1,0))$, $\ \partial\phi_{a}(t,0,1,(1,0))$ and $\ \partial\phi_{b}(t,0,1,(1,0))$, but I don't know what they me to obtain using the differentiable dependence theorem on initial conditions and parameters.
I'd appreciate some hint about it.
Thanks.