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