Question

find the general solution of the differential equation dy/dx=6y^(1/2)

Answer 1

\[
y' = 6\sqrt{y}
\]?

Answer 2

@wio, I don't think that is correct. the answer to a differential equation's general solution should be in terms of y, not y'

Answer 3

Okay well it's separable.

Answer 4

I'm stuck at
\[\int\limits_{}^{}\frac{ dy }{ y^{1/2} } = \int\limits_{}^{}6dx\]
\[2y ^{1/2} = 6x + c\]
I know I need to divide both sides by 2 and then square each side, but does this include the c? (do I do [(6x+c)/2]^2 or just 3x^2 + c?)

Answer 5

you may assume c/2 = C

Answer 6

because the constant can be anything

Answer 7

It's going to be something like \(y=9x^2+6Cx+C^2\)