math

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use implicit differentiation to find dy/dx and then d^2y/dx^2.

y^2=ye^x^2+2x

ans for dy/dx= [2(xye^x^2 + 1)]/(2y-e^x^2)
after that i don't know how to proceed. can someone show me the steps(x need for calculation) and final answer. i try to use wolfram but it give me a weird ans( maybe i don't know how to input this formula).

• math -

It's nasty, but you gotta use the quotient rule, substituting in y' as needed:

y'' =

[[(ye^x^2 + xy'e^x^2 + xy(2xe^x^2))(2y-e^x^2)]
- [(xye^x^2 + 1)(2y' - 2xe^x^2)]]
/ (2y-e^x^2)^2

EEEK! After substituting in for y', it's nasty.

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