6 . Exact Differential Equation
Differential equation M ( x , y ) dy + N ( x , y ) dy = 0 is called an exact differential equation .
If a function u ( x , y ) exist such that , du = Mdx + Ndy .
Necessary and Sufficient Condition for an Equation to be an Exact Differential Equation
Differential equation Mdx + Ndy = 0 where , M and N are the functions • of x and y , will be an exact differential equation , if
∂N / ∂y = ∂N / ∂x
Solution of Exact Differential Equation
7 . Linear Differential Equation
A linear differential equation of the first order can be either of the following forms
( i ) dy / dx + Py = Q , where P and Q are functions of x or constants . ( ii ) dx / dy + Rx = S , where Rand S are functions of
y or constants . Consider the differential Eq . ( i ) i . e ., dy / dx + Py = Q