Find y' y^2 = x cos y assuming that the equation determines a differentiable function f such that y= f(x)
2yy' = (1)(cosy) - (siny)y'(x)
2yy'-x(sin(y))y'=cosy
y'=cosy/(2y-xsiny)

- anonymous

- schrodinger

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- anonymous

just want to check my answer

- anonymous

2y dy/dx = x ( -sin(y) dy/dx ) +cos(y) )

- anonymous

wait, thats wrong

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## More answers

- anonymous

the cos9y) at the end shouldnt be in the bracket

- anonymous

cos(y)

- anonymous

kk its the same as my answer just in terms of dy/dx so its correct :)?

- anonymous

you did make a mistake

- anonymous

aww :(

- anonymous

an algebraic one, not a calculus one

- anonymous

hmm not suprised not a fan of algebra

- anonymous

first line to second line

- anonymous

you take a term from the RHS to the left, but dont change the sign

- anonymous

its suppose to be positive when i take it over?

- anonymous

yeah i just realized

- anonymous

ok thank you

- anonymous

ok thank you

- anonymous

also , just something notation wise,
the first line
2yy' = (1)(cosy) - (siny)y'(x) , is badly written

- anonymous

like I mean I could get what you mean, but be aware of the order of the terms

- anonymous

I know you mean to write -xsin(y) y' for the last term

- anonymous

but you have -sin(y) y'(x)
which can be interperated as -sin(y) dy/dx

- anonymous

it might confuse yourself and the markers, so I would be careful about that in the future , order your terms to eliminate confusion

- anonymous

oh i do it step by step i wrote it that way on my next line sorry

- anonymous

I dont care exactly what you do , I am just saying , I highly recommend you dont put y' and x next to eaach other in a term , especially with the x in a bracket, just remember that y'(x) is an alternative notation for dy/dx

- anonymous

ok thanks for the advice i will remeber it for next time

- anonymous

alternatively , you can just write dy/dx when you use chain rules instead of y' , I rarely write y' , because it doesnt tell what the derivative is with respect to , and once you start to do multivariable calculus then you actually do have to write dy/dx , because y' is meaningless when you have multiple variables

- anonymous

ok

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