Q. 104.0( 33 Votes )

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


Answer :





Here, putting x = kx and y = ky




= k0f(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 ev + v = t


(ev + 1)dv = dt





logt


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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