a. b.
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. This is a Bernoulli Equation. So make the substitution . Then and . Then the DE becomes . This is now first order linear, so use the integrating factor method. The integrating factor is . Multiplying through by the integrating factor gives . Since
how to solve b? i tried to recombinate it into (-xy^2-x^3+x)dx+2y(x^2-1)dy=0 and solve it this way is there any other easier way ?
(b) is also Bernoulli. Multiply by and try letting
in bernulyy method we eliminate y from the right side and if the power of y is 3 then we divide by y^3 and put a new variable v=1/y^2 so we need to divide by y but is our variable
Originally Posted by Danny (b) is also Bernoulli. Multiply by and try letting How can it be Bernoulli? When you multiply by you get , which is not of the correct form ...
Last edited by Prove It; November 14th 2010 at 12:32 AM.
You sure? Look closely.
Well I had a sign wrong, but apart from that, it does not look to be of the correct form...
i am confused when i multiply by y i get a bernully for correct?
Originally Posted by transgalactic i am confused when i multiply by y i get a bernully for correct? As has been said already, you multiply it by y and then make the substitution u = y^2: This is a simple first order ODE solvable using the integrating factor method.
thanks
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