There are 3 methods used to solve differential equations,how can we determine which one from the question?

Asked by Susan fletcher | 18th Feb, 2014, 11:59: AM

Expert Answer:

First find the order and degree of the differential equation.
 
The differential equations of the first order and first degree can be expressed as Mdx+Ndy=0, where, M and N are the functions of x and y.
 
Step 1: Check whether the function is a variable separable one.
That is the differential equation can be expressed as f(x)dx+g(y)dy = 0, where f(x) is a function of x alone and g(y) is a function of y alone.
Step 2: If the function is not variable separable, check whether it is an homogenous equation.
A function of two variables f(x,y) is said to be homogeneous of degree n if we replace both variables x and y by  lambda x space a n d space lambda y,  we find: f open parentheses lambda x comma lambda y close parentheses equals lambda to the power of n f open parentheses x comma y close parentheses
Step 3:If the given equation cannot be solved by variable separable and homogeneous methods, then check whether it can be expressed in the form, fraction numerator d y over denominator d x end fraction plus P y equals Q comma space w h e r e space P space a n d space Q space a r e space f u n c t i o n s space o f space x space a lone comma space or space constants.
Or check whether it can be expressed in the form, fraction numerator d x over denominator d y end fraction plus R x equals S comma space w h e r e space R space a n d space S space a r e space f u n c t i o n s space y space a l o n e space o r space c o n s tan t s.

Answered by  | 18th Feb, 2014, 02:40: PM

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