# Math Help - ODE question!

1. ## ODE question!

The following equation arises in the mathematical modeling of reverse osmosis.
(sin t)y'' - 2(cos t)y' - (sin t)y = 0, 0 < t < pi

Find a general solution. Hint: First observe that y = cos t is as solution, but the sine function is not a solution. To find a second solution, apply the reduction of order technique.

2. Originally Posted by ninano1205
The following equation arises in the mathematical modeling of reverse osmosis.
(sin t)y'' - 2(cos t)y' - (sin t)y = 0, 0 < t < pi

Find a general solution. Hint: First observe that y = cos t is as solution, but the sine function is not a solution. To find a second solution, apply the reduction of order technique.
treat $y = v(t) \cos t$ as the second solution.

now solve for $v(t)$ by treating the above as a particular solution

can you finish?

3. ## Thank you for reply but,

I can't understand what u meant by saying by treating the above as a particular solution?

4. Originally Posted by Jhevon
treat $y = v(t) \cos t$ as the second solution.

now solve for $v(t)$ by treating the above as a particular solution

can you finish?
Originally Posted by ninano1205
I can't understand what u meant by saying by treating the above as a particular solution?
It's fair to assume you've been taught this technique so it should be clear what's meant.

Substitute $y = v \cos t$ into the DE. This will give you (after simplifying) a new DE with v in it. Solve this DE for v.