In each of the question, show that the given differential equation is homogeneous and solve each of them.

Here, putting x = kx and y = ky

= k^{0}f(x,y)

Therefore, the given differential equation is homogeneous.

To solve it we make the substitution.

x = vy

Differentiation eq. with respect to x, we get

Integrating both sides, we get

Put e^{v} + v = t

(e^{v} + 1)dv = dt

logt

log(e^{v} + v)

∴ log(e^{v} + v) = - logy + logC (∴ From (i) eq.)

Multiply by y on both side, we get

ye^{x/y} + x = C

x + ye^{x/y} = C

The required solution of the differential equation.

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