Find the general solution of the differential equation
`log((dy)/(dx))=(ax+by).`

Explanation

`log((dy)/(dx))=ax+by`
`rArr (dy)/(dx)=e^(ax+by)=e^(ax*e^(by))`
`rArr (1)/(e^(by))dy=e^(ax)dx" " `[on separating the variables]
`rArr int e^(-by)dy=int e^(ax)dx " " `[integrating both sides]
`rArr (e^(-by))/(-b)=(e^(ax))/(a)+C`
`rArr ae^(-by)+be^(ax)=C'," where "C'= -abC.`
Thus, `ae^(-by)+be^(ax)=C' ` is the required solution.