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Mathematics
m y d x = n x d y mydx=nxdy
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The given equation is m y d x = n x d y mydx=nxdy.
Solution:
We can rearrange the equation as follows:
d y y = m n d x x (dy)/(y)=(m)/(n)(dx)/(x)
Now we integrate both sides
d y y = m n d x x int(dy)/(y)=int(m)/(n)(dx)/(x)
ln | y | = ln | x | m n + C 1 ln |y|=ln |x|^((m)/(n))+C_(1)
where C 1 C_(1) is the constant of integration.
Taking exponential on both sides,
| y | = e ln | x | m n e C 1 |y|=e^(ln |x|^((m)/(n)))e^(C_(1))
| y | = C | x | m n |y|=C|x|^((m)/(n))
where C = e C 1 > 0 C=e^(C_(1)) > 0 is the constant of integration.
Therefore, the solution to the differential equation is | y | = C | x | m n |y|=C|x|^((m)/(n)).
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