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Semaj Christian

Semaj Christian

Answered question

2022-06-20

Given that f : is invertible, differentiable and monotonic increasing.
Need to find a general solution for the equation:
f ( y ) y = x f ( y )
I'm working to either separate variables or to put the equation in linear form of y but no success so far.

Answer & Explanation

kpgt1z

kpgt1z

Beginner2022-06-21Added 23 answers

Hint:
f ( y ) y = x f ( y )
f ( y ) f ( y ) d y = x d x
ln | f ( y ) | = x 2 2 + constant
f ( y ) = C e x 2 / 2
y = f 1 ( C e x 2 / 2 )
You have to justify the validity of the main steps.

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