HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

Determine the order and degree of the following differential equation:

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

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

Find the differential equation whose general solution is

x³ + y³ = 35ax.

Solve the following differential equation.

`dy/dx + y` = 3

The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.

The solution of `dy/ dx` = 1 is ______.

A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.

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

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

Solve: `("d"y)/("d"x) + 2/xy` = x² 

Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is

The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.

A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution

The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation

Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______

State whether the following statement is True or False: 

The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any

State whether the following statement is True or False:  

The degree of a differential equation `"e"^(-("d"y)/("d"x)) = ("d"y)/("d"x) + "c"` is not defined

State whether the following statement is True or False:

Order and degree of differential equation `x ("d"^3y)/("d"x^3) + 6(("d"^2y)/("d"x^2))^2 + y` = 0 is (2, 2)