1.

Find the general solution of each of the following differential equations: `x(x^(2)-x^(2)y^(2))dy +y(y^(2)+x^(2)y^(2))dx =0`

Answer» Correct Answer - `(-1)/(2y^(2))-(1)/(2x^(2))+log|(x)/(y)|=C`
`x^(3)(1-y^(2))dy +y^(3)(1+x^(2))dx =0 rArr int ((1-y^(2)))/(y^(3))dy + int ((1+x^(2)))/(x^(3)) dx = C.`
`therefore int (y^(-3)-(1)/(y)) dy +int (x^(-3)+(1)/(x))dx = C rArr (y^(-2))/(-2)-log|y|+(x^(-2))/(-2) +log|x|=C.`


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