# Thread: separation of variables (calculus)

1. ## separation of variables (calculus)

ok, so how does one attempt this using separation of variables?:

y' = the square root of ty

so far, what i have done is set y' equal to t^(1/2) * y^(1/2) since the square root of two variables is just the square root of each individual variable.

i'm not really sure what to do after that so i would be grateful for any help!

2. Originally Posted by clockingly
ok, so how does one attempt this using separation of variables?:

y' = the square root of ty

so far, what i have done is set y' equal to t^(1/2) * y^(1/2) since the square root of two variables is just the square root of each individual variable.

i'm not really sure what to do after that so i would be grateful for any help!
you were right so far. Now just divide both sides to obtain

y'/y^(1/2) = t^(1/2) or equivalently y^(/1/2) dy = t^(1/2) dt

now integrate both sides

2y^(1/2) = (2/3)t^(3/2) + C
=> y = [{(2/3)t^(3/2) + C}^2]/2

3. Originally Posted by Jhevon
you were right so far. Now just divide both sides to obtain

y'/y^(1/2) = t^(1/2) or equivalently y^(/1/2) dy = t^(1/2) dt

now integrate both sides

2y^(1/2) = (2/3)t^(3/2) + C
=> y = [{(2/3)t^(3/2) + C}^2]/2