Differential Equations - 16 - Exact with Integrating Factor EXAMPLE

Example, demonstrating how to solve a non exact differential equation using an integrating factor

[TheLazyEngineer]

MISTAKE!!! At 6:30 I use (x^2 + xy) when I should have used the expression WITH the integrating factor which is: (x^3 + x^2y). Other than that, the process is correct. To correct this error, simply set x^3 + x^2y + g'(y) = x^3 + x^2y at 6:36

[sudhirsharma]

really amazing....cleared my week points.

[parkerromanek]

Since x^3 + x^2y + h’(y) = x^3 +x^2y, h’(y) = 0 and h(y) = C correct?

[SachinJadhav-pw]

If we divide the equation by xy we find that the equation is homogeneous. Why do you say its not homogeneous?

[isaacdesantigoisaac]

why did you use the first experessios of psi "y" that we had before multiplying by our integratig factor instead of the other one?, i mean, before multiplying by these factor the equation was not exact. If you do like i say, the derivate of g(y) is equal to 0, ad in effect g(y)=c

[lokeshiitdelhi]

Your solution is actually wrong you missed x to multiply on LHS I can't figure out in which step you have made the mistake. But solving the solution again you won't get the initial differential equation we have.