Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Find `bb(dy/dx)` in the following:

`y = sin^(-1)((2x)/(1+x^2))`

Show that the given differential equation is homogeneous and solve them.

(x² + xy) dy = (x² + y²) dx

Show that the given differential equation is homogeneous and solve them.

`y' = (x + y)/x`

Show that the given differential equation is homogeneous and solve them.

(x – y) dy – (x + y) dx = 0

Show that the given differential equation is homogeneous and solve them.

(x² – y²) dx + 2xy dy = 0

Show that the given differential equation is homogeneous and solve them.

`x^2 dy/dx = x^2 - 2y^2 + xy`

Show that the given differential equation is homogeneous and solve them.

`x  dy - y  dx =  sqrt(x^2 + y^2)   dx`

Show that the given differential equation is homogeneous and solve them.

`{xcos(y/x) + ysin(y/x)}ydx = {ysin (y/x) -  xcos(y/x)}xdy`

Show that the given differential equation is homogeneous and solve them.

`x dy/dx - y +  x sin (y/x) = 0`

Show that the given differential equation is homogeneous and solve them.

`y  dx + x log(y/x)dy - 2x  dy = 0`

Show that the given differential equation is homogeneous and solve them.

`(1+e^(x/y))dx + e^(x/y) (1 - x/y)dy = 0`

For the differential equation find a particular solution satisfying the given condition:

(x + y) dy + (x – y) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

x² dy + (xy + y²) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

`[xsin^2(y/x - y)] dx + x  dy = 0; y = pi/4 "when"  x = 1`

For the differential equation find a particular solution satisfying the given condition:

`dy/dx -  y/x + cosec (y/x) = 0; y = 0` when x = 1

For the differential equation find a particular solution satisfying the given condition:

`2xy + y^2 - 2x^2  dy/dx = 0; y = 2`   when x  = 1

A homogeneous differential equation of the from `dx/dy = h (x/y)` can be solved by making the substitution.

Which of the following is a homogeneous differential equation?

Prove that x² – y² = c (x² + y²)² is the general solution of differential equation  (x³ – 3x y²) dx = (y³ – 3x²y) dy, where c is a parameter.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is `4/27 pih^3` tan²α.