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Words 282

Pages 2

Excellent does not an accident, but it comes through a hard work!!

Condition for exact equation: M ( x, y )dx N ( x, y )dy 0 is called an EXACT EQUATION if and only if M N y x

Excellent does not an accident, but it comes through a hard work!!

GOAL

By comparing M ( x, y )dx N ( x, y )dy 0 with F F dx dy dF x y

F ( x, y) c

F M x

F N y

Test for exactness

F M N F yx y x xy

2 2

Excellent does not an accident, but it comes through a hard work!!

1) Write

F F M (1) and N (2) x y

4) Compare eqn(4) with eqn(2) to obtain ( y)

2) Integrate eqn(1) w.r.t x, so F x dx M dx ( y) F ( x, y ) M dx ( y ) (3) where ( y ) is a function of y alone.

5) Integrate ( y) w.r.t y to get the unknown ( y )

6) Substitute ( y) into eqn(3) in order to complete the required solution.

3) Differentiate eqn(3) w.r.t y F Mdx ( y ) (4) y y

Let’s Try

Excellent does not an accident, but it comes through a hard work!!

Solve this differential equation: (e ye ) dx (e xe )dy 0; y x x y

y (1) 0

Excellent does not an accident, but it comes through a hard work!!

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