If the family of straight lines in the \( x-y \) plane satisfying the property that the sum of \( x \) and \( y \) intercepts on co-ordinate axes is 2020 has differential equation \( \left(x \frac{d y}{d x}-y\right)\left(\frac{d y}{d x}-1\right)+k \frac{d y}{d x}=0 \) then the value of \( \frac{k}{404} \) is equal to \( (5) \)

Question

If the family of straight lines in the \( x-y \) plane satisfying the property that the sum of \( x \) and \( y \) intercepts on co-ordinate axes is 2020 has differential equation \( \left(x \frac{d y}{d x}-y\right)\left(\frac{d y}{d x}-1\right)+k \frac{d y}{d x}=0 \) then the value of \( \frac{k}{404} \) is equal to