Solve the following initial value problem: `x(dy)/(dx)+1=0; y(-1)=0`

Answer

`y=-log x`

Explanation

We are given

`x(dy)/(dx)+1=0`


`xfrac{ d y}{d x}=-1`


`rArr frac{d y}{d x}=-\frac{1}{x}`


Now separate variables

`d y=-\frac{1}{x} d x`

Integrate both sides we get,


`y=-\log x+c` , where `c` is the constant term


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