Integrating Factor Assignment Help

Assignment Help: >> Differential equation >> Integrating Factor

Integrating Factor:

A factor, which when multiplied to non exact, differential equation makes it exact, is called as integrating factor for example the non exact equation y dx -x dy = 0 can be made exact on multiplying by factor 1/y2 . Therefore 1/y2 is the integrating factor for this equation.

Notes:

Generally such a factor exists but except in certain special cases, it is difficult to determine. The number of integrating factor for the equation M dx + N dy = 0 is infinite.

Some of the Useful Results are stated below:

d(xy) = xdy + ydx

39_Integrating Factor.png

Example: Solve  x dy - y dx  = 812_Integrating Factor1.png.

 Solution:     

                   771_Integrating Factor2.png

                    113_Integrating Factor3.png

                    64_Integrating Factor4.png

                      2432_Integrating Factor5.png

 

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