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

Determine the order and degree (if defined) of the differential equation:

`(d^2y)/(dx^2)^2 + cos(dy/dx) = 0`

Determine the order and degree (if defined) of the differential equation:

`(d^2y)/(dx^2)` = cos 3x + sin 3x

Determine the order and degree (if defined) of the differential equation:

( y′′′) + (y″)³ + (y′)⁴ + y⁵ = 0

Determine the order and degree (if defined) of the differential equation:

y′′′ + 2y″ + y′ = 0

Determine the order and degree (if defined) of the differential equation:

y′ + y = e^x

Determine the order and degree (if defined) of the differential equation:

y″ + (y′)² + 2y = 0

Determine the order and degree (if defined) of the differential equation:

y″ + 2y′ + sin y = 0

The degree of the differential equation `((d^2y)/(dx^2))^3 + ((dy)/(dx))^2 + sin ((dy)/(dx)) + 1 = 0` is ______.

The order of the differential equation `2x^2 (d^2y)/(dx^2) - 3 (dy)/(dx) + y = 0` is ______.

For the differential equation given below, indicate its order and degree (if defined).

`(d^2y)/dx^2 + 5x(dy/dx)^2 - 6y = log x`

For the differential equation given below, indicate its order and degree (if defined).

`((dy)/(dx))^3 -4(dy/dx)^2 + 7y = sin x`

For the differential equation given below, indicate its order and degree (if defined).

`(d^4y)/dx^4 - sin ((d^3y)/(dx^3)) = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

xy = a e^x + b e^-x + x² : `x (d^2y)/(dx^2) + 2 dy/dx - xy + x^2 - 2 = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = e^x (acos x + b sin x)  :  (d^2y)/(dx^2) - 2 dy/dx + 2y = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = xsin 3x   :   (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`

For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`x^2 = 2y^2 log y : (x^2  + y^2) dy/dx - xy = 0`

Find the rate of change of the area of a circle with respect to its radius r when r = 3 cm.

The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an edge is 12 cm?

The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?