Question

Prove x^2 (dy/dx) - xy = 1 + cos(y/x) is a homogeneous differential equation.

Answer 1

do u know whats homogeneous diff equation?

Answer 2

yes

Answer 3

whats ur definition of homogeneous diff equation?

Answer 4

If \[\frac{ dy }{ dx } = \frac{ M(x,y) }{ N(x,y) }\]
then
its said to be in homogeneous form

Answer 5

a function f(x,y) is said to be a homogeneouss de of degree n if f(ax,ay)=a^n f(x,y) for any non zero constant a

Answer 6

yes

Answer 7

how do you get f(ax,ay)=a^n f(x,y) here

Answer 8

see i divided by x^2 here. everything's okay except for the 1/x^2.

Answer 9

here its not a polynomial to have f(ax,ay)=a^n f(x,y)
in differential eqautions its different

Answer 10

Its not a homogeneous diff equation

Answer 11

it came in todays foreign cbse board paper.