Solve the following differential equations: `y-x(dy)/(dx)=a(y^2+(dy)/(dx))`

Explanation

Given

`y-x(dy)/(dx)=a(y^2+(dy)/(dx))`
`implies (dy)/(dx)(a+x)=y-(dy)^2`

`implies ((dy)/(y-ay^2))=((dx)/(a+x))`

`implies ((dy)/(y(1-ay)))=((dx)/(a+x))`

`implies ady(1/(ay)+1/(1-ay))=((dx)/(a+x))`

`implies ln(y)+(aln(1-ay))/(-a)=ln(a+x)`

`implies ln |y| =ln|1-ay|`

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