Question

The above question. I have tried it a couple of times and have reached the end but the answer comes out to be -2y, maybe some arithmetic errors. What’s the solution?

Answer 1

Given-----> ( x - y ) e^ ( x/ x - y ) = a

To prove -----> y dy/dx + x = 2y

Proof ------> 1) plzzz see the attachement

2) ATQ,

( x - y ) e^ ( x / x - y ) = a

Then we take log both sides and using

a) log ( m . n ) = logm + logn

b) log ( mⁿ ) = n logm

c) loge = 1

3) Then differentiating with respect to x by using

a) d/dx ( u/v ) = v du/dx - u dv/dx / v²

b) d/dx ( x ) = 1

c) d/dx ( c ) = 0

and solving we get the desired result