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joyce945
30.06.2019 •
Mathematics
Solve 3x^2-y^2)dx+(xy-x^3y^{-1})dy=0 through homogenous equations i've gotten to y(y^2-3x^2)/x(y^2-x^2) but don't know what to do from there
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Ответ:
The integrating factor will be in the form:
This gives:
Now set partial derivatives equal to find a,b.
Setting coefficients equal we have:
Solving this system of 2 equations yields:
Now you have an exact diff equation:
The solution is:
h(y) and h(x) are constants in terms of the specified variable.
By equating the 2 integrals, you can see that
Finally, the general solution is:
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