 # Differential Equation Class 12 Notes Chapter 9

## What are differential equations?

The equation which involves the derivative of the variable which is dependent with respect to the independent variable is known as the differential equation. The order here is given to the highest order of the occurring derivative. The degree is given to the presence of the polynomial equation in the derivatives. ### What are the solutions?

The function which is able to satisfy the given differential equation is known as the solution. A general solution is referred to the presence of many arbitrary constants in their order, and if the solution is free from these arbitrary constants, then it is called a particular solution. In order to form a differential equation from a function which is given, the function should be differentiated several times as the number of arbitrary constants present in the function and then eliminated at last.

### Variable Separation Method

This type of method is used to solve certain types of equations in which the variables can be separated entirely, which means the terms which contain y should have dy, and the terms which contain x should have dx.

### Homogenous Differential Equation

When the zero-degree homogenous functions can be expressed in the form dy/dx=f(x,y) or dx/dy=g(x,y) where f(x,y) and g(x,y) are the mentioned functions, then it is called homogenous differential equations.

### First Order Linear Differential Equations

If R and S are the constants or functions of x only and the differential equation is of the form dy/dx+Ry=S.

 Also Access NCERT Solutions for Class 12 Maths Chapter 9 NCERT Exemplar for Class 12 Maths Chapter 9

### Important Questions

1. What will be the population of the village in 2019 if the population of the village was 30 000 in 1888 and 20000 in the year 2003? The rate of increase of the population is continuously at a rate proportional to the number of its inhabitants present at any time.
2. Find the equation of the curve passing through the point (0, π/6), and the differential equation is sin y cos z dx + cos y sin z dy = 0.
3. If in the first quadrant, a family of circles touches the coordinate axes. Form the differential equation for it.
4. If the slope of the tangent to the curve at any point (p, q) is equal to the sum of the coordinates of the point, then find the equation of a curve passing through the origin.
5. If the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5 then find the equation of a curve passing through the point (0, 5) given that.

 Differential Equation Solution of Separable Differential Equation

## Frequently Asked Questions on CBSE Class 12 Maths Notes Chapter 9 Differential Equations

Q1

### What is a differential equation?

A differential equation is a mathematical equation that involves variables like x or y, as well as the rate at which those variables change.

Q2

### What are the uses of calculus?

Calculus has applications in various fields, such as engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

Q3

### What are the uses of differential calculus?

1. Rate of change of a quantity with respect to another 2. To find if a function is decreasing or increasing 3. To find the maximum and minimum value of a curve