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Solve the following differential equation.
y dx + (x  y^{2} ) dy = 0
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Solution
y dx + (x  y^{2} ) dy = 0
∴ y dx = (y^{2}  x) dy
∴ `dx/dy = (y^2  x) /y= y  x/y `
∴ `dx/dy + x/y = y`
The given equation is of the form
`dx/dy + Px = Q`
where, P = `1/y` and Q = y
∴ I.F. = `e int^ (pdy) = e int ^(1/ydy) = e ^(log y)= y`
∴ Solution of the given equation is
`x (I.F.) =int Q (I.F.) dy + c_1`
∴ `xy = int y(y) dy = y^3/3 + c_1`
∴ 3xy = y^{3} + c …[3c_{1} = c]
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