Question

solve xyp^2-(x^2+y^2)p-xy=0​

Answer 1

Explanation:

The given differential equation is

xyp2 – (x2 + y2)p + xy = 0

xyp2 – x2p – y2p + xy = 0

px(py – x) – y(py – x) = 0

(px – y)(py – x) = 0

(px – y) = 0, (py – x) = 0

When (px – y) = 0

(dyx/dx) – y) = 0

(dx/x) – (dy/y) = 0

Integrating, we get

log x – log y = log c

x = cy

When (py – x) = 0

(y(dy/dx) – x) = 0

xdx – ydy = 0

Integrating, we get

x2 – y2 = a2

Hence, the required solution is

(xy – c)(x2 – y2 – a2) = 0

Answer 2

Answer:

xyp^2-(x^2-y^2)p+xy=0