Hi

My question is

Consider the initial value problem

$\displaystyle yy'=x-1$

subject to the intitial condition $\displaystyle y(x=X)=Y$ where X and Y are constants.

a)For which values of X and Y does the existence and uniqueness theorem ensure the existence of a unique solution? If a unique solution can be shown to exist, will it exist for all values of $\displaystyle x$.

b)Find thegeneralsolution of the ODE, using any suitable method.

In my notes i have a section on uniqueness of solutions but its not very detailed. It mentions Peano existence theorem and also mentions picard existence theorem.

I wanted to know what the difference what between these two theorems also.

thanks