Solve the following differential equation: `y-x(dy)/(dx)=b\ (1+x^2 \ (dy)/(dx))`

Explanation

`y-x \frac{d y}{d x}=b(1+x^{2} \frac{d y}{d x}) `

` y-b=(x+b x^{2}) \frac{d y}{d x}`

`frac{d x}{x(1+b x)}=\frac{d y}{y-b} `

`int(\frac{1}{x}-\frac{b}{1+b x}) d x=\log (y-b)+\log c `

`log x-\log (1+b x)=\log (y-b)+\log c `

`frac{x}{c}=(1+b x)(y-b) `

`b+(\frac{1}{c}+b^{2}) x=y(1+b x) `

`b+kx=y(1+b x)`