Uniqueness of Solution for y' = y(siny) + x with Initial Value of f(0) = -1

[cragar]

Homework Statement

y' = y(siny) + x does this have a unique solution ,
with the intial value of f(0)= -1

The Attempt at a Solution

the partial dervative with respect to y is
del(x)/del(y) = siny + cosy(y) this is continuous on the rectangle including
(0 , -1 ) so this is unique.

is this right

 

[HallsofIvy]

Yes, that is correct. Strictly speaking, for uniqueness you only requrire that f(x,y), in dy/dx= f(x,y), be "Lischitz" in y but that is implied by continuous derivative so that is sufficient.

 

[cragar]

im just curious do you have your ph.d. in math