Day: February 29, 2016

Existence and uniqueness for differential equations

Existence and uniqueness for differential equations

Existence and uniqueness for differential equations   02/29/16

 

One of the quandaries that a student of mathematics must face is proving existence and uniqueness for differential equations. Suppose we come across a differential equation dydx=f(x,y)with the initial value y(a)=b. If we want to prove that a solution exists for some xvalue, then we just have to discern if f(x,y)is continuous “near” some value (a,b) then a solution does in fact exist. Furthermore, if we would like to find if the solution is unique same near the same (a,b) value we have to take the partial derivative f(x,y)yand observe if it is continuous near (a,b)