Practicing Success
The solution of the differential equation y' = (x+y)/x is- |
y = 2x log x + Cx y = -x log x + Cx y = x log x + Cx y = x log x - Cx |
y = x log x + Cx |
The given differential equation is y' = (x+y)/x which can be written as dy/dx = (x+ y)/ x.....................(i) This is an homogeneous differential equation. Let y = vx ⇒dv/dx = v + x (dv/dx) substituting the values of v and dv/dx in equation (i) we get: v+ x (dv/dx) = {x +(vx)}/x ⇒ v + x(dv/dx) = (1+v) ⇒dv = dx/x on integrating both sides, we get: v = xlogx + C since v= y/x ⇒ y/x = xlogx +c ⇒ y = x log x + Cx
|