I am trying to evaluate the equation: y &#x2032; </msup> = y (

enthral4kvri

enthral4kvri

Answered question

2022-06-04

I am trying to evaluate the equation:
y = y ( y 2 1 2 )
I multiplied the y over and tried to solve it in seperable form (M and N). The partial deritives did not work out to be equal to eachother so I am now stuck finding an integrating factor. Is this the right approach?

Answer & Explanation

Lovedalefpblz

Lovedalefpblz

Beginner2022-06-05Added 1 answers

Separation will work, just that partial fractions have to be dealt with:
1 y ( y 2 1 / 2 ) d y = 1 d x
( 4 y 2 y 2 1 2 y ) d y = 1 d x
ln ( 2 y 2 1 ) 2 ln y = ln 2 y 2 1 y 2 = x + K
2 y 2 1 y 2 = 2 1 y 2 = A e x
y = ± 1 2 A e x
Ada Harper

Ada Harper

Beginner2022-06-06Added 2 answers

This is also a Bernoulli equation, set u = y 2 to get
u = 2 y 3 y = 2 + u u = 2 + C e x ( u 0 2 ) y ( x ) = y 0 2 y 0 2 + ( 1 2 y 0 2 ) e x

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