Find the particular solution of the differential equation given that when [CBSE 2016]

Given equation:

2ye^x/ydx + (y - 2ye^x/y)dy = 0

⇒ …(1)

Let

⇒

Then,

⇒

Let x = vy

Differentiating wrt y, we get

⇒

Substituting the value of x and dx/dy in eqn(1), we get

⇒

⇒

⇒

⇒

⇒

⇒

Substituting the value of v, we get

⇒ …(2)

Substituting x = 0 and y = 1 in equation (2), we get

⇒

Substituting the value of C in equation (2), we get

⇒

Which is the particular solution of the given differential equation.