Question

Which of the following is a homo-geneous differential equation?
(a) (11x + 5y + 8) dy-(y + x-2) dx = 0
(b) xạy dx -(x - y)dy
(c) (x - y) dy =(x + 2y) dx
(d) (x3 + 2y2) dx = -2xy dy​

Answer 1

Answer:

xy

2

dy−(y

3

−2x

2

)dx=0

dx

dy

=

xy

2

y

3

−2x

3

Put y=vx

dx

dy

=v+x

dx

dv

v+x

dx

dv

=

x

y

−2

y

2

x

2

=u−

v

2

2

x

dx

dv

=

v

2

−2

v

2

dv=−2

x

dx

3

v

3

=−2logx+logC

3

v

3

=

x

2

c

y

3

=3cx