Question

Difference between homogeneous and linear differential equation

Answer 1

Hey!
here is ur answer....

Firstly, you have to understand aboutDegree of an eqn. Basically, the degree is just the highest power to which a variable is raised in the eqn, but you have to make sure that all powers in the eqn are integers before doing that.
For eg, degree of the equaytion
 x^2 + x=0
is 2, since 2 is the highest power x is raised to.
Now, coming to your question:

Linear equations:

Linear eqns are those whose degree is 1  .
Similarly, equations of any other degree are called non linear.
Particularly, equations of 2nd degree are called quadratic and those of fourth degree are called cubic eqns.

Homogeneous equations:

So far we have discussed only equations in 1 variable( x in the example I used)
In eqns of 2 or more variables, the equation is said to be homogeneous if, thedegrees of all terms in an eqn are one and the same. 
For eg, consider an eg. of an eqn in two 


So , as you see, all terms in the eqn have same degree, ie, 3 . Hence it is homogeneous .

hope so it helped u...please mark it....