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this is my first attempt at using the latex commands ..

consider this Cauchy Problem:

[tex]

u_x\exp y +u_y\exp(x)=1

[/tex]

[tex]

u(t,tk^2)=k\exp(-t)

[/tex]

where k is a constant.

forgive me i have given up using latex as i am too slow, it would take me a week to type it up at this rate. anyway

i am trying to find the values of k where

a) this problem has a unique solution

b) no solutions

for part a) i know that it all boils down to showing where the vector (1,k^2) is never parallel to ( exp(t*k^2), exp(t) )

i eventually get to:

t cant be equal to 2ln(k)/(1-k^2), however the question asks for values of k and i havent done that. but i dont know any way to find explicit values of k

for part b) i just said t=2ln(k)/(1-k^2)

is it reasonable to give the answer in the form i have? i'm not sure

hope you can help

thanks,

vladimir

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# Finding if a solution exists

Can you offer guidance or do you also need help?

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