Science (English Medium) Class 12 - CBSE Question Bank Solutions

The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.

Solution of differential equation xdy – ydx = 0 represents : ______.

Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.

Solution of the differential equation tany sec²xdx + tanx sec²ydy = 0 is ______.

Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.

Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.

The number of solutions of `("d"y)/("d"x) = (y + 1)/(x - 1)` when y (1) = 2 is ______. 

tan^–1x + tan^–1y = c is the general solution of the differential equation ______.

The general solution of e^x cosy dx – e^x siny dy = 0 is ______.

The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.

Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.

The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.

The integrating factor of the differential equation `("d"y)/("d"x) + y = (1 + y)/x` is ______.

y = ae^mx+ be^–mx satisfies which of the following differential equation?

The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.

The solution of `x ("d"y)/("d"x) + y` = e^x is ______.

The general solution of `("d"y)/("d"x) = 2x"e"^(x^2 - y)` is ______.

The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.

The solution of the equation (2y – 1)dx – (2x + 3)dy = 0 is ______.

The differential equation for which y = acosx + bsinx is a solution, is ______.