y dy = x dx + x^3 dx
y^2/2 = x^2/2 + x^4/4 + c
Dy/dx=(X+x^3)/y
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4 answers
It might be easier to break-up the fraction then take the derivative of each:
(X+x^3)/y ==> x/y + x^3/y
Dy/dx = 1/y + 3x^2/y = 3x^2/y
(X+x^3)/y ==> x/y + x^3/y
Dy/dx = 1/y + 3x^2/y = 3x^2/y
What Damon did was the anti-derivative or indefinite integral. Dy/dx is Leibniz's notation which means you are taking the derivative of y with respect to x. It is the prime notation for the derivative of a function. The second answer would be correct. 3x^2/y is the derivative of your function.
I think Damon is right on this, otherwise, the equals sign is meaningless.