Differential Equation:Non Exact first order ODE into exact form: Example Integrating factor RULE III

If you need to hire services for language tutoring, website designing, logo making, video animation, search engine optimization, and much more, then please click the following links, you’ll find qualitative and reliable services at reasonable rates;

Please watch: "Limit of a function f(x): Epsilon ϵ and Delta δ definition with example"

Non-Exact First Order Ordinary Differential Equations: Example Integrating factor Rule III:-

If a differential equation of the form
M(x,y) dx + N(x,y) dy=0
is not exact as written, then there exists a function μ( x,y) such that the equivalent equation obtained by multiplying both sides of (*) by μ,

μM dx + μN dy =0
is exact. Such a function μ is called an integrating factor of the original equation and is guaranteed to exist if the given differential equation actually has a solution. Integrating factors turn non-exact equations into exact ones. The question is, how do you find an integrating factor?

RULE III:-
Consider the differential equation M dx + N dy = 0. If this equation is not exact, then M y will not equal N x ; that is, M y – N x ≠ 0. However, if
xM+yN ≠ 0
Then reciprocal of xM+ yN will help us in getting integrating factor.

Non-Exact First Order Ordinary Differential Equations: Example Integrating factor Rule II:

How to solve first order ordinary Exact differential equations: Explanation & Example:



"Ordinary Differential Equations ODEs: Solving ODE through Method of separating variables examples"

"First order ordinary homogeneous differential equations: Transforming into separable equations e.g."

"First Order Ordinary Differential Equations Reducible to Homogeneous Form (Case I) Example"

"First Order Ordinary Differential Equations Reducible to Homogeneous Form (Case II):"

Integration by parts:-