Class 12 maths exercise 12.5 solution with pdf

Homogeneous Differential Equation 

(1) Homogenous Function. 

A Function is said to be homogenous of the nth degree in x and y if it can be put in the form xnf[y/x]

Alternatively, a function f (x,y) is said to be homogeneous of degree n if f(x,y) = n f(x,y) for any non zero constant. 

for example  

  f(x,y) = (3x+2y) + x[3+2y/x] , is homogeneous function of degree 1. 

(2)  Homogeneous Differential Equation. 

A differential equation in x and y is said to be a homogeneous differential equation if it can be put in the form dy/dx  = f1(x,y)/f2(x,y) , where f1(x,y) and f2(x,y) are homogeneous functions of the same degree in x and y 

for example 

dy/dx = y2-x2 /2xy is a homogeneous equation since y2 - x2 and 2xy are both homogeneous function of degree 2 

Exercise 12.5 complete solution in pdf download pdf and make study easy

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