HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Important Questions

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

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 ______.

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 ______.

The integrating factor of `(dy)/(dx) + y` = e^–x 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.

The rate of growth of population is proportional to the number present. If the population doubled in the last 25 years and the present population is 1 lac, when will the city have population 4,00,000?

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:

The integrating factor of `("d"^2y)/("d"x^2) - y` = e^x, is e^–x, then its solution is

Choose the correct alternative:

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