Arts (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

`int (x + 3)/(x + 4)^2 "e"^x  "d"x` = ______.

Find the differential equation of the family of curves y = Ae^2x + B.e^–2x.

Find the differential equation of the family of lines through the origin.

Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.

Find the equation of a curve passing through the point (1, 1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

If A and B are invertible matrices of the same order, then (AB)^-1 is equal to ____________.

The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.

The differential equation representing the family of curves y = A sinx + B cosx is ______.

Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.

Find the equation of a curve passing through origin and satisfying the differential equation `(1 + x^2) "dy"/"dx" + 2xy` = 4x² 

Form the differential equation by eliminating A and B in Ax² + By² = 1

Find the differential equation of system of concentric circles with centre (1, 2).

Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is `(x^2 + y^2)/(2xy)`.

Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is `(y - 1)/(x^2 + x)`

Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.

Find the equation of a curve passing through the point (1, 1). If the tangent drawn at any point P(x, y) on the curve meets the co-ordinate axes at A and B such that P is the mid-point of AB.

Family y = Ax + A³ of curves is represented by the differential equation of degree ______.

The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.

The differential equation of the family of curves x² + y² – 2ay = 0, where a is arbitrary constant, is ______.

Family y = Ax + A³ of curves will correspond to a differential equation of order ______.