SOLUTION: In the given equation below, α is the value that will make the equation exact. Find 2α - α^2. 2xy^3 - 3y - (3x + αx^2y^2 - 2αy) y’ = 0

Algebra ->  Finance -> SOLUTION: In the given equation below, α is the value that will make the equation exact. Find 2α - α^2. 2xy^3 - 3y - (3x + αx^2y^2 - 2αy) y’ = 0      Log On


   

Question 1165588: In the given equation below, α is the value that will make the equation exact. Find 2α - α^2.
2xy^3 - 3y - (3x + αx^2y^2 - 2αy) y’ = 0
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
2xy%5E3++-++3y++-++%283x+%2B+alpha%2Ax%5E2y%5E2++-++2%2Aalpha%2Ay%29%2A%22y%27%22+=+0

2xy%5E3++-++3y++%2B++%28-3x+-+alpha%2Ax%5E2y%5E2++%2B++2%2Aalpha%2Ay%29%2A%22y%27%22+=+0



%282xy%5E3++-++3y%29dx++%2B++%28-3x+-+alpha%2Ax%5E2y%5E2++%2B++2%2Aalpha%2Ay%29dy+=+0

M(x,y)=2xy³-3y 
N(x,y)=-3x-αx²y²+2αy

∂M/∂y = 6xy²-3
∂N/∂x = -3-2αxy²

These will be equal and the differential equation will be exact iff:

-2α = 6
  α = -3

I guess you didn't want to solve the exact differential equation.

2α-α² = 2(-3)-(-3)² = -6-(9) = -15

Edwin