Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Form the differential equation having y = (sin^–1x)² + Acos^–1x + B, where A and B are arbitrary constants, as its general solution.

Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.

Find the general solution of y²dx + (x² – xy + y²) dy = 0.

Solve:

`2(y + 3) - xy  (dy)/(dx)` = 0, given that y(1) = – 2.

Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`

Solve the differential equation (1 + y²) tan^–1xdx + 2y(1 + x²)dy = 0.

Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`

Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.

Find the general solution of `("d"y)/("d"x) -3y = sin2x`

If y = e^–x (Acosx + Bsinx), then y is a solution of ______.

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 ______.