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(x^2+2y^2) dx/dy = xy || Homogeneous Substitution
Автор: Jonathan Walters
Загружено: 2021-03-29
Просмотров: 12910
Описание:
We solve the equation (x^2+2y^2) dx/dy = xy using a Homogeneous Substitution y = ux.
We actually first check to see if the equation is exact.
After showing it is not exact, we show that it satisfies the definition of a homogeneous equation by showing M and N are both homogeneous functions of the same degree.
The substitution process involves substituting
y = ux and
dy = udx + xdu
We then make and cancellations and separate the variables for integration.
As always if you have any questions, feel free to comment down below!
-Jonathan
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