Question

solve the differential equation th-ye dr.
Traz dy = 0, y (o)= 3 by Sepana
of vaniablea​

Answer 1

Answer:

Consider the problem

y

2

dx+(3xy−1)dy=0

y

2

dx=(1−3xy)dy

dy

dx

=

(y

2

)

1

−

y

3x

dy

dx

+

y

3x

=

y

2

1

Which is a linear differential equation of the form

dy

dx

+P(y)x=Q(y)

Now,

Integrating factor =e

(∫P(y)dy)

=e

(∫

y

3

dy)

=y

3

Multiplying both sides by integrating factor

y

3

(

dy

dx

)+3y

2

x=y

Now,

dy

d

[xy

3

]=y

Integrating both sides.

xy

3

=

2

y

2

+C