# What is the particular solution of the differential equation? : # dx/(x^2+x) + dy/(y^2+y) = 0 # with #y(2)=1#

# y= (x+1)/(2x-1) #

We have an differential equation equation in the form of differentials:

We can write this in "separated variable" form as follows and integrate both sides

Leading to:

Thus:

Using this in the above we get:

We can now evaluate the integrals (not forgetting the constant of integration) to get:

Then rearranging and using the properties of logarithms we have:

Thus the required solution is:

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It is a Separable Variable Type Diff. Eqn., &, to obtain its

General Solution (GS), we integrate term-wise.

To find its Particular Solution (PS), we use the given IC, that,

This gives us the complete soln. of the eqn. :

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The particular solution of the given differential equation is ( y(x) = \frac{1}{x+1} ).

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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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