List of top Mathematics Questions on Differential equations asked in AMUEEE

The equation of the curve satisfying the differential equation $ y(x+y^3)dx = x(y^3- x)dy $ and passing through the point $ (1, 1) $ is

Let $ f(x) $ be differentiable on the interval $ (0, \infty) $ such that $ f(1) = 1 $ and $ lim_{t \rightarrow x} \frac {t^2f(x)-x^2f(t)}{t-x} =1 $ for each $ x>0 $ . Then, $ f(x) $ is

Which of the following is a correct solution of $ x\,cosx\,\left(\frac{dy}{dx}\right) + y(x sin x +cos x) = 1 ? $