Solve the following differential equation:` x y dy=(y-1)(x+1)dx`

Explanation

`x y d y=(y-1)(x+1) d x`


separate the variables


`Rightarrow frac{y}{y-1} d y=frac{x+1}{x} d x`


Integrate both sides


`int frac{y}{y-1} d y=int frac{x+1}{x} d x`


`Rightarrow int frac{y-1+1}{y-1} d y=int frac{x+1}{x} d x`


`Rightarrow int d y+int frac{1}{y-1} d y=int d x+int frac{1}{x} d x`


`Rightarrow y+log |y-1|=x+log |x|+C`


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