# How do you solve the differential #y'xln(x)=y#?

To make ln x real, x > 0.

Separating variables and integrating,

So,

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To solve the differential equation ( y'x\ln(x) = y ), you can use the method of separating variables. Rearrange the equation to isolate the variables ( y ) and ( x ), and then integrate both sides. The solution is:

[ y = Cx ]

where ( C ) is the constant of integration.

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To solve the differential equation ( y'x \ln(x) = y ), you can use separation of variables method. First, rewrite the equation in the form ( \frac{dy}{dx} = \frac{y}{x \ln(x)} ). Then, separate the variables ( y ) and ( x \ln(x) ) and integrate both sides with respect to their respective variables. This will involve integrating ( \frac{1}{y} , dy ) on one side and integrating ( \frac{1}{x \ln(x)} , dx ) on the other side. After integrating, solve for ( y ) to find the general solution of the differential equation.

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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.

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