MATH201 Lecture Notes - Lecture 3: Slope Field, Implicit Function
24 Aug 2016
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Definition: the function is called a solution for the problem if there exists an interval for some a>0, such that (i) (ii) , where satisfies the initial conditions for all , we have , where satisfies the de. Claim 1: is the solution of the given graph with. Example 3: consider the following second order ivp. Claim 3: is a solution to the problem. Remark: sometimes, the solution cannot be written in explicit form , the solution is obtained in the implicit form. Example 1: consider the following initial value problem. Claim 1: the implicit function is a solution to the problem. Is the following a solution to the problem? (true or false) Definition: the de of the form (that f doesn"t have x explicitly) called autonomous equation (first order); otherwise (f having x explicitly) is called non-autonomous! Definition: consider the following autonomous equation ; the value (numbers) y is called an equilibrium for the problem if.
