CBSE Class 12 Mathematics — Differential Equations

The integrating factor of differential equation $R\left(\frac{dx}{dy}\right) + Px = Q$, where P, Q, R are functions of y, is

The order and degree of the differential equation $\frac{d}{dx}(e^y) = 0$ respectively are

(a) Find the general solution of the following differential equation: $x^2 \frac{dy}{dx} = x^2 + xy + y^2$ OR (b) Find the particular solution of the differential equation $xy \frac{dy}{dx} = (x + 2)(y + 2)$, given that $y(1) = -1$.