MATH 046 Lecture 5: Classification of First Order Equations
Document Summary
Any(cid:1) rst(cid:1) order(cid:1) ordinary(cid:1) di erential(cid:1) equation(cid:1) can(cid:1) be(cid:1) written(cid:1) as y (x) = f (x, y(x)) for such function f (x, y) of two variables. This is called the standard form of a rst order ordinary di erential equation. We can also write the equation simply as where we understand that y is the unknown function and x is the variable. y = f (x, y) Example(cid:1) (1) (2) is a rst order ordinary di erential equation in the standard form. y = sin(xy) + y2 exy + y(x) = sin(x) is not in the standard form. To write the equation in the standard form, we rst subtract y from both side and divide by ex. The result is y = sin(x) y ex. Write(cid:1) the(cid:1) following(cid:1) equation(cid:1) in(cid:1) the(cid:1) standard(cid:1) form. Answer(cid:1) to(cid:1) in(cid:1) class(cid:1) exercise(cid:1) is the same as. Y2 = 0. xy = y2. y = y2 x.
