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

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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)   (Show Source): You can put this solution on YOUR website!








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
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