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Solve the following differential equations (i) (dy)/(dx) = (x^(2)+y^(2))/(2x^(2)) (ii) y^(2)dx + (x^(2) - xy)dy = 0 (iii) (dy)/(dx) = ((x+y)^(2))/(2x^(2)) (iv) (dy)/(dx) = (x-y)/(x+y) (v) (x^(2) + y^(2)) dy = 2xydx (vi) (x^(2) - y^(2))dx - xydy = 0

Answer»


Answer :(i) `2x = (x-y)(log x + c)` (ii) `ky = e^((y)/(x))`
(iii) `log x = 2Tan^(-1)((y)/(x)) + c`
(iv) `x^(2) - 2xy - y^(2) = c`
(v) `K(x^(2) - y^(2)) = y` (vi) `x^(2)(x^(2) - 2Y^(2)) = k`


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