How to start learning Differential Equations
Class 12 Maths-Differential Equations
I am Suman Mathews, math teacher and content developer. Having taught Mathematics for over three decades, to High school and college students, I can help you with the study of Differential equations. Spend 15 minutes at least reading this and utilise the youtube links at the end of this post which has a variety of free lectures and multiple choice questions.
These are the topics which I will be teaching in my online classes together with problem solving.
What are Dependent and Independent variables in Differential Equations?
First, you need to understand the concept of dependent and independent variable. Given dy/dx, y is the dependent variable and x is the independent variable. Again, in dx/dy, x is the dependent variable and y is the independent variable. An equation which involves unknown functions and their derivatives with respect to one or more independent variables is called a differential equation. An equation which involves unknown functions containing only one independent variable and their derivatives with respect to that independent variable is called an ordinary differential equation. In Class 12, we deal with the study of ordinary differential equations.
What do you mean by the order of a Differential equation?
The order of a differential equation is the highest order derivative of the dependent variable with respect to the independent variable. If each term involving the derivatives of a differential equation is a polynomial or can be expressed as a polynomial, then the highest exponent of the highest order derivative is called the degree of the differential equation. You need to understand the difference between the general solution and a particular solution of a differential equation.
MCQ Degree of a Differential equation
The general solution of a differential equation of order one contains one arbitrary constant. Any solution which is obtained from the general solution by giving particular values to the constant is called a particular solution. While solving a differential equation, there are a few types that you need to keep in mind.
What is the Variables Separables method in Differential Equations?
Variables Separables method- In differential equations of this type, you can separate the variables and then integrate. This is the easiest method of integrating a differential equation and can be used in most problems. You can also reduce an equation to the variables separables form by a simple substitution. Find the solution of this Differential Equation
What is a Homogeneous Differential Equation?
First and foremost, you'll need to identify a homogenoeus differential equation. This can be done by a simple test. Once you do that, there are two types of homogeneous differential equations, each of which use a similar yet slighlty different method to solve. Basically using these substitutions, you convert a homogeneous equation to the varisble separables form and then solve.
What are Linear Differential equations?
Linear Differential Equations
A linear equation of the form dy/dx+P(x) y = Q(x) is a linear differential equation.To solve a linear differential equation, you'll first need to calculate the integrating factor. Once you do this, you can solve using the formula. Again there are two types of linear differential equations and each of then use a similar, yet slightly different technique for solving.
Keep in mind that for a linear differential equation, you will write the constant c as soon as you write the general solution. In other integration problems, we write the constant c only after removing the integral sign.
Yet another important factor is finding the particular solution. When the initial value conditions are given, after finding the general solution of the differential equation, you'll need to substitute these values and find c.
Do you still need more help in Differential Equations Class 12 Maths?
All the above topics will be taught in detail in my online classes. You can contact me for online classes if you need more help. I can help prepare you for your exams with adequate training in multiple choice questions, concept based questions and Case study based questions. Practice tests on Differential equations is also available. There are a number of free resources here in the form of youtube videos. You can access these at no extra cost.
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