(a) Write the order and degree of the differential equations. xy(d^2y/dx^2)^2 + x (dy /dx)^3 - y (dy/dx) = 0

Question

(a) Write the order and degree of the differential equations.

\(xy(\frac{d^2y}{dx^2})^2\) + \(x(\frac{dy}{dx})^3\) - \(y(\frac{dy}{dx})\) = 0

(b) Find the general solution of the differential equation ylog ydx – xdy = 0

(c) Find the integrating factor of the differential equation

\(x\frac{dy}{dx} - y = 2x^2\)

Answer 1

(a) order : 2; degree : 2

(b) y log ydx - xdy = 0

integrating on both sides;

⇒ logx = log (log y) + log c

⇒ logx = log(clog y)

⇒ x = c log y.