Solve the following differential equations.
(i) `(dy)/(dx) =(1+y^(2))/(1+x^(2))` (ii) `(dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2)))`
(iii) `(dy)/(dx) = 2y tan hx`
(iv) `sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0`
(v) `(dy)/(dy) = e^(x-y)+x^(2)e^(-y)`

Answer

(i) `tan^(-1)x = tan^(-1) y+c`
(ii) `sin^(-1)y = sin^(-1)x + c`
(iii) `y = C cos h^(2)x`
(iv) `xsqrt(1+x^(2))+ysqrt(1+y^(2)) + sin h^(-1) x + sn h^(-1) y = c`
(v) `e^(y) = e^(x) + (x^(3))/(3) + c`