HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

Solve the differential equation (x² + y²)dx- 2xydy = 0

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`

If the population of a country doubles in 60 years, in how many years will it be triple under
the assumption that the rate of increase in proportional to the number of inhabitants?
[Given : log 2 = 0.6912 and log 3 = 1.0986.]

Find the area of the region bounded by the curves y² = 4x and 4x² + 4y² = 9 with x > = 0.

Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`

Determine the order and degree of the following differential equation:

`[1 + (dy/dx)^2]^(3/2) = 8(d^2y)/dx^2`

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = A cos (log x) + B sin (log x)

Solve the following differential equation:

cos x . cos y dy − sin x . sin y dx = 0

Solve the following differential equation:

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

Solve the following differential equation:

(x² + y²)dx - 2xy dy = 0

Solve the following differential equation:

`x * dy/dx - y + x * sin(y/x) = 0`

Solve the following differential equation:

`x^2.  dy/dx = x^2 + xy + y^2`

Solve the following differential equation:

(x² – y²)dx + 2xy dy = 0

The differential equation `y dy/dx + x = 0` represents family of ______.

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.

The general solution of `(dy)/(dx)` = e^−x is ______.

Select and write the correct alternative from the given option for the question 

Differential equation of the function c + 4yx = 0 is

Select and write the correct alternative from the given option for the question

The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively

Select and write the correct alternative from the given option for the question

The solution of `("d"y)/("d"x)` = 1 is

State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x