Solve the differential equation #2xlnx dy/dx + y = 0#?
# y = A/sqrt(lnx) #
We have:
We can use an integrating factor when we have a First Order Linear non-homogeneous Ordinary Differential Equation of the form;
So rewrite the equations in standard form as:
Then the integrating factor is given by;
Which we can rearrange to get:
Which, is the General Solution.
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The solution to the differential equation (2x \ln(x) \frac{dy}{dx} + y = 0) is given by:
[y = Cx^{-2}]
where (C) is an arbitrary constant.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- What is the area of the region in the first quadrant bounded on the left by the y-axis, below by the line y = x/4, above left by the curve y=1 + sqrt(x), and above right by the curve y=2\/sqrt(x)?

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