SOLUTION: use the differential equation given by dy/dx=xy/3, y > 0. Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4.

Algebra ->  Finance -> SOLUTION: use the differential equation given by dy/dx=xy/3, y > 0. Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4.      Log On


   

Question 1032274: use the differential equation given by dy/dx=xy/3, y > 0.
Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 4.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The differential equation dy%2Fdx=%28xy%29%2F3 becomes dy%2Fy+=+%28x%2F3%29dx
==> lny+=+x%5E2%2F6+%2B+c for some undetermined constant c.
y%5B0%5D+=+f%280%29+=+4 ==> lny = 0 + c = c ==>lny+=+x%5E2%2F6+%2B+ln4, or
ln%28y%2F4%29+=+x%5E2%2F6. (Notice the restriction to the y-values y > 0.)
In exponential form, the solution is y+=+4e%5E%28x%5E2%2F6%29, or y+=+4exp%28x%5E2%2F6%29.