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Question
`(x + 2y^3 ) dy/dx = y`
Solution
`(x + 2y^3 ) dy/dx = y dx/dy`
∴`x/y + 2y^2 = dx/dy`
∴ `dx/dy - x/y = 2y^2`
The given equation is of the form
`dx/dy + px =Q`, where, `P = -1/ y and Q = 2y^2`
∴ I.F. `= e ^(int^(pdy) = e^ (-int^(1/y dy)`
`= e ^(-logy) = e^(1/y)`
`=1/y`
∴ Solution of the given equation is
`x(I.F.) = intQ(I.F.) dy + c`
∴ `x/y =2 int y^2/y d y +c `
∴ `x/y= 2 int y dy +c `
∴ `x/y= 2 y^2/2 +c `
∴ x = y(c + y2)
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