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how to convert explicit function to implicit?

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M
M 2021-8-21
评论： M 2021-8-21
Hi, I have an equation and I want y be as a fuction, in fact, I 'd like a function in which x is independent variable and y is dependent to x,could you please help me how to do it?
A is a complicated equation but doesn't have "y" in it so it is not important what it is, a and b also have values.
  2 个评论
Rik
Rik 2021-8-21
This seems doable with fairly basic algebra. What have you tried so far?
M
M 2021-8-21
it seems simple but when I tried to solve by hand, it becomes complicated...

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Wan Ji
Wan Ji 2021-8-21
If you feel bored solving it by hand, just use matlab!
syms a y x b A
eq = a*y - x*(a+1) - A*(x^2-b*a^2*(y-x)^2);
y = solve(eq, y)
the answer is
y =
-((4*b*A^2*x^2 + 4*b*A*x + 1)^(1/2) - 2*A*a*b*x + 1)/(2*A*a*b)
((4*b*A^2*x^2 + 4*b*A*x + 1)^(1/2) + 2*A*a*b*x - 1)/(2*A*a*b)

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