Here, putting x = kx and y = ky
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 ev + v = t
(ev + 1)dv = dt
log(ev + v)
∴ log(ev + v) = - logy + logC (∴ From (i) eq.)
Multiply by y on both side, we get
yex/y + x = C
x + yex/y = C
The required solution of the differential equation.
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