Question

Differential equation dy/dx=y/x​

Answer 1

Answer:

dy/dx = y/x

dy/y = dx/x

integrate

Always remember integration of 1/x is log x

So, log y = log x + log c ( take constant as log c)

log y - log x = logc

log (y/x) = log c

Compare

y/x = c

y= CX

#answerwithquality #BAL

Answer 2

Answer:

We can separate the variables:

d

y

d

x

=

y

x

⇒

d

y

y

=

d

x

x

Integrate both sides:

∫

d

y

y

=

∫

d

x

x

⇒

ln

(

y

)

=

ln

(

x

)

+

C

So:

y

=

e

ln

(

x

)

+

C

=

e

ln

(

x

)

⋅

e

C

=

C

x