Question

if the general solution of the diff. eq. y'=y/x +f(x/y), for some function y,is given by yln|cx|=x ,where c is an arbitary constant,then f(2)=?

Answer 1

tried this?

find y' from ln|cx|=x

plug it in diff. eq.

put x = 2y

Answer 2

the variable y remains in the eq..

Answer 3

y' ln |cx| + y/x = 1

y' = (1-y/x)/ ln |cx|

but ln |cx| = y/x

y' = (1-y/x)/(y/x)

y' = y/x + f(x/y)

(1-y/x)/(y/x) = y/x + f(x/y)

x= 2y, y/x = 1/2

(1-1/2)/(1/2) = 1/2 + f(2)

Answer 4

oh ok i didn't substitute..ln|cx|=y/x..

Answer 5

thank u @hartnn !

Answer 6

welcome ^_^