Differential Equations Notes for IIT JEE, Download PDF!

By Subrato Banerjee|Updated : December 15th, 2018

Differential equations is a scoring topic from JEE Main point of view as every year 1 question is certainly asked. Every candidate should take care of not letting go easy marks from this topic. To revise effectively read and revise from the Differential Equations Short Notes. You can also download Indefinite Integration notes PDF at end of the post.

1. Differential Equations

A differential equation is a just as a normal equation consists of variables and numeric constants. The only difference in between the normal equation and differential equation is that the former contains one variable and constants whereas, in the differential equation, it consists of independent variables, dependent variables, and numeric constants only.

NOTE: Numeric constant means numbers

Examples of the differential equation:



2. Order and degree of a differential equation

Order of differential equation is defined as the highest number of times the dependent variable is differentiated with respect to the independent variable.

The degree of a differential equation is defined as the highest power of the highest order differential variable in the equation.

For example: in the equation, 5the order is 3 and the degree is 1.

3. Formation of a differential equation from a given equation

Whenever an equation is given, choose the dependent variable and independent variable.

Then differentiate the equation with respect to the independent variable. Now try and eliminate the constants and variables other than the dependent and differential term.

NOTE: Differentiate the equation as many numbers of variable or constants in the equation

Example: (ax+y2) =0. Find differential form

On differentiating w.r.t x we get


So, 7

Thus, substituting in parent equation we get


4. General format of First order differential form


(a). Variable Separable form

If the equation is given in the form

10and such that 12

Then this technique is applicable


Solution: Now we can separate in the following format


Integrating both sides, we get

ey=ex + C

(b) Differential equations reducible to a separable variable type

If the given equation is in the form of

13; Then apply this technique.

Put ax+by=t , then differentiating we get 14

Substitute value of t and 15in terms of16and solve the given problem. 





Let x+2y=t


Putting in the equation


Now integrate both sides to get



A function f(x) is said to be in homogeneous form if the independent variable can be expressed in terms of the dependent variable and vice-versa.

In this type consider y=vx and hence21

Substitute these values in the equation and obtain the result.

6. Exact Differential form

Certain differential equation need not be rearranged or solved using the first-order solving technique.

They can be integrated directly to obtain the result

For example:




Thus integrating w.r.t x

We, get


7. First order Linear Differential form

The general format of the equation is in the form


This is a must format and the technique could be applied only when this form is satisfied.

Now we need to find the Integration Factor (I.F.)=25

Now multiply each term with the I.F.

Hence we get


Now by exact form, the LHS can be converted as


Now integrate both sides to obtain the required result.

For example:


IF=e∫2 dx


Thus our next form becomes


Thus our equation becomes


Thus solution becomes

x=ye2x + C

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dude shriyansh
Sir can we have vectors,3-D revision notes
Premsay Shyamle
Hindi language me

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