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Solve the following differential equatio...

Solve the following differential equations (i) `(1+y^(2))dx = (tan^(-1)y - x)dy`
(ii) `(x+2y^(3))(dy)/(dx) = y`
`(x-(1)/(y))(dy)/(dx) + y^(2) = 0`
(iv) `(dy)/(dx)(x^(2)y^(3)+xy) = 1`

Text Solution

Verified by Experts

The correct Answer is:
(i) `x e^(tan^(-1)y) = e^(tan^(-1)y)(tan^(-1)y-1)+c`
(ii) `x = y(y^(2) + c)`
(iii) `xy = 1+ y + cy e^((1)/(y))`
(iv) `1+x(y^(2) - 2+ce^(-y^(2)//2)) = 0`
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