## Question

using the transformation x=r cosθ and y=r sinθ,find the singular solutionof the differential equation x+py=(x-y)(p^{2}+1)½ where p=dy/dx

**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

x=rcosθ and y=rsinθ

so dx=-rsinθdθ and dy = rcosθdθ

so p = -cotθ

so given eq. will become x-cotθy = (x-y)cosecθ

on putting values of x and y we get

0 = r(cosθ-sinθ)/sinθ

so tanθ = 1 so θ = nπ+π/4

so x = rcos(nπ+π/4) and y = rsin(nπ+π/4)