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Semaj Christian 2022-06-20 Answered
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.
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Answers (1)

kpgt1z
Answered 2022-06-21 Author has 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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