Question

calculate the derivative of y in respect to x
x^(3)y+3xy^(3)=x+y

Answer 1

x³y + 3xy³ = x + y
3x²y + x³y ' + 3( y³+ 3xy²y') = 1 + y'
( x³ + 9 xy² - 1) y' = 1 - 3y ( x² + y² )
=> y' = 1 - 3y ( x² + y² ) / ( x³ + 9 xy² - 1)