Question

How do you find the differential of the function `y dy/dx=(x+3)(y^2+3)` ?

Answer 1

See below.

Explanation:

Assuming that we ask for the differential equation solution, after observing that the differential equation is separable, we can arrange it as

`(y dy)/(y^2+3) = (x+3) dx` and after integration gives

`1/2log_e(y^2+3) = 1/2 x^2+3x + C_0` or

`log_e(y^2+3)=x^2+6x+C_1` or

`y^2 +3 = C_2e^(x^2+6x)` or

`y = pm sqrt( C_2e^(x^2+6x)-3)`