How do you find the particular solution to #2xy'lnx^2=0# that satisfies y(1)=2?
Use the separation of variables method.
Integrate.
Use
Separate variables:
Integrate:
The particular solution is:
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To find the particular solution to the differential equation (2xy'  \ln(x^2) = 0) that satisfies the initial condition (y(1) = 2), you can follow these steps:

First, rewrite the equation in the form (y' = f(x,y)) to separate variables.

Solve the resulting firstorder ordinary differential equation for (y) in terms of (x).

Integrate both sides of the equation to find the general solution, including a constant of integration.

Apply the initial condition (y(1) = 2) to determine the value of the constant of integration and obtain the particular solution.
By following these steps, you can find the particular solution that satisfies the given initial condition.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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