Find the general solution of each of the following differential equations:
`(1+x^(2))(dy)/(dx)=xy`

Answer

`y=C_(1)sqrt(1+x^(2))`

Explanation

`int (1)/(y)dy=(1)/(2) int (2x)/((1+x^(2)))dx rArr log|y|-(1)/(2)log|1+x^(2)|=log|C|`
`rArr log|(y)/(sqrt(1+x^(2)))|=log|C| rArr (y)/(sqrt(1+x^(2))) = pm C = C_(1).`