Consider the coupled nonlinear system of equations given by x^3+e^y=s, cosx+xy=t which we wish to be able to solve uniquely for (x,y) in terms of (s,t). Show this cannot be done at (x,y)=(0,0)

dansleiksj

dansleiksj

Answered question

2022-09-05

Consider the coupled nonlinear system of equations given by
x 3 + e y = s               cos x + x y = t
which we wish to be able to solve uniquely for ( x , y ) in terms of ( s , t ). Show this cannot be done at ( x , y ) = ( 0 , 0 ).

Answer & Explanation

Preston Buckley

Preston Buckley

Beginner2022-09-06Added 5 answers

Compute the total differentials:
3 x 2 d x + e y d y = d s , sin x d x + y d x + x d y = d t .
At ( x , y ) = ( 0 , 0 ),
0 d x + d y = d s , 0 d x + 0 d y = d t .
The Jacobian matrix of the transform is singular.

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