Solutions Of Differential Equations

The given differential equation is xdy - ydx = 0. We can rewrite it as:

x(dy) = y(dx)

Separating variables, we get:

dy/y = dx/x

Integrating both sides, we have:

∫(dy/y) = ∫(dx/x)

Logarithmic integration gives:

ln|y| = ln|x| + C, where C is the constant of integration.

Exponentiating both sides to eliminate the natural logarithm, we get:

|y| = e^C * |x|

Replacing e^C with a new constant K, this becomes:

y = Kx

The equation y = Kx is the equation of a straight line passing through the origin with slope K. Hence, the general solution of the given differential equation represents a straight line passing through the origin.