find the general soln of dy/dx = (2x^3 + 6)/y

find the general solution of the differential solution

dy/dx = (2x^3 + 6)/y

dy/y = 2x^3 +6dx

im stuck after this i knw you have to take the integral of each but how do i take the intergral of dy/y

The integral of dy/y is just \(\displaystyle \L\\\int\frac{1}{y}dy\)

You know what that integral is, I bet.

the integral of dy/y = ln y + C
but this is not relative to your problem

dy/dx= [2x^3+6] / y
multiply both sides of the = sign with y
y [dy/dx]= [2x^3+6]
multiply both sides of the = sign with dx
y dy =[2x^3+6] dx
integrate
y^2 /2 = 2x^4/4 +6x
multiply both sides by 2
y^2=x^4 +12x
y^2=x[x^3+12]

Arthur

Thank you!