`xy' + y = xy^3` Solve the Bernoulli differential equation.

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Given equation is `xy' + y = xy^3`

An equation of the form `y'+Py=Qy^n`

is called as the Bernoullis equation .

so, to proceed to solve this equation we have to transform the equation into a linear equation form of first order as follows

=>` y' (y^-n) +P y^(1-n)=Q`

let `u= y^(1-n)`

=> `(1-n)y^(-n)y'=(u')`

=> `y^(-n)y' = (u')/(1-n)`

so ,

`y' (y^-n) +P y^(1-n)=Q`

=> `(u')/(1-n) +P u =Q `

so this equation is now of the linear form of first...

(The entire section contains 282 words.)

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