HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Important Questions

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

Form the differential equation of y = (c₁ + c₂)e^x 

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Solve: `("d"y)/("d"x) + 2/xy` = x²