# 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.

- What is the general solution of the differential equation? : # (d^2y)/dx^2-dy/dx-2y=4x^2 #
- What is a particular solution to the differential equation #(du)/dt=(2t+sec^2t)/(2u)# and #u(0)=-5#?
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- How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=5e^(x)# and #y=5e^(-x)#, x = 1, about the y axis?
- 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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