# What is a particular solution to the differential equation #dy/dx=cosxe^(y+sinx)# with #y(0)=0#?

this is separable!!

and this is separated, so next...integrate each side wrt x

but before we do that, just note that

OR

if you see that, brilliant. the job is done!

if not :-((

So, to tidy it all up....

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The particular solution to the given differential equation ( \frac{dy}{dx} = \cos(x)e^{y+\sin(x)} ) with the initial condition ( y(0) = 0 ) is ( y = \ln(\cos(x)+1) - \sin(x) ).

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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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