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

Solve the following differential equation:

`dy/dx + y/x = x^3 - 3`

Solve the following differential equation:

`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`

Solve the following differential equation:

dr + (2r cotθ + sin2θ)dθ = 0

In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.

If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.

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 

Write the degree of the differential equation (y''')² + 3(y") + 3xy' + 5y = 0

Solve the differential equation

`y (dy)/(dx) + x` = 0

Form the differential equation of all lines which makes intercept 3 on x-axis.