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What is the best way to learn differential equation in easier way? Can you please let me know the answer on the same? How can I learn it quick and in smarter way? Can you please give me the suggestion which would help me to come over this?

'Differential Equations' is one of the most interesting topics in Mathematics and Algebra.

First of all, you must build up your interest in Study of Calculus.

Clear all the concepts of Derivatives and Integration and then move on to Differential Equations. This will make the things much easier.

Now to learn Differential Equations easily, you can simply split the topics and further break down their types and remember them.

Differential Equations Chapters basically include 3 types of questions:

1) Finding Order and Degree of Differential Equations.
2) Removing Arbitrary Constants from equations.(Also forming Differential equations).
3) Solving Differential Equations.

Out of these three, students feel Difficulty in solving the equations.
Process of solving these Equations at Basic level include three major ways:

1) Variable Separation.
2) Homogeneous Solution.
3) Linear Method ( Also called P.Dx method by many) .

Now you have a clear image of basic things you have to do in Differential equations.

You will have to recognize the questions type and use one of three methods accordingly.

Getting better at doing these include only one way that is Practising Practising and practicing.

Pick up various books like R.D Sharma , Moderns and keep only solving questions and you will get better at doing those.

Note: This chapter stands one two legs, and we can call those legs as Derivatives and Integrals. If you don't know them ,you won't be good at this chapter too.

( Source : Have been doing this topic recently )