(x^2-2xy)dx+(siny-x^2)dy=0 #ExactEquation L522 @MathsPulseChinnaiahKalpana

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Here is a video of Exact equation problem. Performing partial derivative of M and N, also integration as well under certain conditions. Please do watch the video till end to learn better.

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Chinnaiah Kalpana🍁

Note:

* Let M(x,y)dx+N(x,y)dy=0 be a first order and first degree differential equation where M, N are real valued functions.

* Working rule for solving an Exact differential equation:

1. Compare the given equation with Mdx+Ndy=0 and find out M and N.

2. Given equation will be exact if partial derivative of M w.r.t y = partial derivative of N w.r.t x.

3. Integrate M partially w.r.t x, treating y as constant.

4. Integrate only those terms of N, which do not contain x, w.r.t y.

5. Equate the sum of the results obtained from (3)&(4) to a constant to obtain required solution.

Therefore, the general solution of the given exact differential equation is
Result obtained from (3) + Result obtained from (4) = c.
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Видео (x^2-2xy)dx+(siny-x^2)dy=0 #ExactEquation L522 @MathsPulseChinnaiahKalpana канала Maths Pulse - Chinnaiah Kalpana